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Justia Dockets & Filings Ninth Circuit California Northern District Cognizant Technology Solutions U.S. Corporation v. McAfee Filing 38
Cognizant Technology Solutions U.S. Corporation v. McAfee
ORDER GRANTING IN PART 36 APPLICATION FOR ATTORNEY'S FEES AND COSTS by Hon. William H. Orrick. Cognizant's motion for attorney's fees and costs is GRANTED in part and DENIED in part. McAfee shall pay Cognizant $124,906.18 in fees and $5,435.55 in costs, totaling $130,341.73. The bond of $100.00 that Cognizant posted shall also be returned. (jmdS, COURT STAFF) (Filed on 8/7/2014)
1 2 3 4 UNITED STATES DISTRICT COURT 5 NORTHERN DISTRICT OF CALIFORNIA 6 7 COGNIZANT TECHNOLOGY SOLUTIONS U.S. CORPORATION, 8 Plaintiff, 9 10 United States District Court Northern District of California 11 v. JOHN MCAFEE, Case No. 14-cv-01146-WHO ORDER GRANTING IN PART APPLICATION FOR ATTORNEY'S FEES AND COSTS Re: Dkt. No. 36 Defendant. 12 13 INTRODUCTION 14 Plaintiff Cognizant Technology Solutions U.S. Corporation ("Cognizant") is seeking 15 attorney's fees and costs for a three-month long case in which it obtained a default judgment. The 16 defendant did not appear and no motions were opposed. Cognizant requests $158,678.51. 17 Under Civil Local Rule 7-1(b), I find this matter suitable for disposition without oral 18 argument and VACATE the hearing currently scheduled for August 13, 2014, and I GRANT in 19 part the application for attorney's fees and costs. While this case was unusual because of the 20 difficulty in serving the defendant, the underlying legal issues were not complicated, especially for 21 a firm of the caliber of the plaintiff's counsel. Cognizant's counsel failed to establish entitlement 22 to, and the reasonableness of, many time entries because of insufficient descriptions, redacted 23 entries, and unreasonable time devoted to certain tasks. I am reducing the award to $130,341.73. 24 25 FACTUAL BACKGROUND Cognizant filed a complaint for violations of Sections 32 and 43(a) of the federal Lanham 26 Act and California Business & Professions Code § 14247 against defendant John McAfee d/b/a 27 Future Tense Central ("McAfee") on March 11, 2014. It made numerous attempts to serve 28 McAfee with the complaint, summons, and other documents. It attempted personal service on 1 McAfee at two separate residences in California. It also attempted to give notice of the action to 2 McAfee by overnight mail at two additional addresses—one in Oregon and one in Colorado—as 3 well as by email and through his personal website. Cognizant made several other unsuccessful 4 attempts to serve McAfee at various addresses. 5 McAfee failed to appear to oppose a temporary restraining order sought by Cognizant and 6 failed to respond to an order to show cause why a preliminary injunction should not issue. On 7 April 4, 2014, I deemed McAfee served. On June 13, 2014, on Cognizant's motion, I entered 8 default judgment against McAfee. 9 Cognizant now moves for attorney's fees and costs. It requests attorney's fees of $153,242.96 for 275.5 hours of attorney time, $3,863.90 of taxable costs, $1,571.65 of non-taxable 11 United States District Court Northern District of California 10 costs, and return of the $100.00 bond posted by Cognizant. Rodrigues Decl. ¶ 37. 12 LEGAL STANDARD 13 "[T]he fee applicant bears the burden of establishing entitlement to an award and 14 documenting the appropriate hours expended and hourly rates." Hensley v. Eckerhart, 461 U.S. 15 424, 437 (1983). "When it sets a fee, the district court must first determine the presumptive 16 lodestar figure by multiplying the number of hours reasonably expended on the litigation by the 17 reasonable hourly rate." Intel Corp. v. Terabyte Int'l, Inc., 6 F.3d 614, 622 (9th Cir. 1993). 18 "Hours that are not properly billed to one's client also are not properly billed to one's adversary 19 pursuant to statutory authority." Hensley v. Eckerhart, 461 U.S. 424, 434 (1983) (original 20 emphasis) (citation omitted). "The district court [ ] should exclude from this initial fee calculation 21 hours that were not 'reasonably expended.'" Id. "Cases may be overstaffed, and the skill and 22 experience of lawyers vary widely," so a court must exclude fees for hours that are "excessive, 23 redundant, or otherwise unnecessary." Id. 24 Where appropriate, "the district court may adjust the 'presumptively reasonable' lodestar 25 figure based upon the factors listed in Kerr v. Screen Extras Guild, Inc., 526 F.2d 67, 69-70 (9th 26 Cir. 1975)." Secalt S.A. v. Wuxi Shenxi Const. Mach. Co., Ltd., 668 F.3d 677, 689 (9th Cir. 2012). 27 The Kerr factors include: "(1) the time and labor required, (2) the novelty and difficulty of the 28 questions involved, (3) the skill requisite to perform the legal service properly, (4) the preclusion 2 1 of other employment by the attorney due to acceptance of the case, (5) the customary fee, (6) 2 whether the fee is fixed or contingent, (7) time limitations imposed by the client or the 3 circumstances, (8) the amount involved and the results obtained, (9) the experience, reputation, 4 and ability of the attorneys, (10) the 'undesirability' of the case, (11) the nature and length of the 5 professional relationship with the client, and (12) awards in similar cases." Kerr, 526 F.2d at 70. DISCUSSION 6 The fact that there is no party to challenge an application for attorney's fees and costs does 7 8 not mean that a court should rubber-stamp the request. On the contrary, it may be even more 9 imperative for a court to scrutinize such a motion. My task is to multiply the number of hours reasonably expended in this litigation by the 10 United States District Court Northern District of California 11 reasonable hourly rate in order to calculate the presumptively reasonable lodestar figure. To the 12 extent that my consideration of the Kerr factors has not already been subsumed in the initial 13 lodestar calculation, I may then adjust the lodestar figure up or down based on the Kerr factors. 14 I. THE HOURLY RATES ARE REASONABLE. Cognizant's counsel, the law firm of DLA Piper, is a large, multi-office firm with multiple 15 16 practices, including an Intellectual Property & Technology Practice Group and a Litigation 17 Practice Group. See generally Rodrigues Decl. ¶¶ 11-23. The hourly billing rate for individuals 18 staffed on this action range from a high of $650.00 for partner Leon Medzhibovsky to a low of 19 $263.50 for senior paralegal Jeff Reeves. Rodrigues Decl. ¶¶ 12, 23. The attorneys staffed on this 20 case are based in New York City and the Bay Area. See generally Rodrigues Decl. ¶¶ 11-23. I 21 find that the hourly rates are reasonable. 22 II. THE REASONABLENESS OF THE HOURS EXPENDED. 23 Although this case was unusual insofar as the defendant attempted to evade service, the 24 underlying matter was a straightforward trademark infringement case. The allegation was that 25 McAfee was releasing a downloadable application using a name "identical" to Cognizant. 26 Compl. 1. Cognizant sought a temporary restraining order and preliminary injunction—both 27 governed by familiar standards. There was no discovery or active motion practice. I granted the 28 unopposed application for a temporary restraining order. Cognizant provided two status updates 3 1 on its attempts to serve McAfee, after which I deemed him served. I then granted a preliminary 2 injunction and entry of default judgment against McAfee. Cognizant now files this motion for 3 attorney's fees. 4 5 While I recognize the quality of the work performed and the success achieved, the request suffers from several deficiencies that warrant adjustment of the award from what is requested. 6 A. Insufficient Billing Descriptions 7 Between February 26, 2014, and February 28, 2014, Cognizant's counsel billed 10.5 hours 8 at a rate of $433.50 in three separate entries for work by "specialist" James Brachulis. All three 9 entries simply state that he conducted "[d]ue diligence per request of Mr. Medzhibovsky related to J. McAfee" without further explanation of what precisely was done. Rodrigues Decl. Ex. B at 4. 11 United States District Court Northern District of California 10 As the Ninth Circuit has explained, a fees request must contain "sufficient detail that a neutral 12 judge can make a fair evaluation of the time expended, the nature and need for the service, and the 13 reasonable fees to be allowed." United Steelworkers of Am. v. Ret. Income Plan For Hourly-Rated 14 Employees of ASARCO, Inc., 512 F.3d 555, 565 (9th Cir. 2008) (citation omitted). This set of 15 requests does not meet that standard and does not allow the Court to adequately assess the 16 reasonableness of the fee request. Counsel billed $4,551.75 for these entries. I will deduct half of 17 this amount, totaling $2,275.88. 18 An attorney, Rajiv Dharnidharka, has numerous billing entries that merely state that 19 "attention" was given to some subject without further description about what effort was expended 20 or what task was accomplished. Examples include "Attention to service of process strategy and 21 temporary restraining order strategy" or "Attention to McAfee complaint and cease and desist 22 letter," but nowhere is there any indication of what was done. These can be contrasted with other 23 entries that provide more meaningful descriptions, such as "Teleconference with Attorneys 24 Medzhibovsky and Rodrigues" and "Review and analyze complaint against Mr. McAfee for 25 trademark infringement." The "attention" entries almost all involve increments of 0.2 or 0.3 26 hours. One entry simply states "Attention to Mr. McAfee's failure to file an opposition to OSC 27 regarding preliminary injunction and strategy for reply brief," which apparently took nearly a third 28 of an hour to complete. Rodrigues Decl. Ex. B at 19. Another entry billed time for giving 4 1 attention to the "order reassigning matter to Judge Orrick"—a one-page form order issued by the 2 Clerk of the Court that merely states that the matter is now before me. Rodrigues Decl. Ex. B at 9; 3 Dkt. No. 11. 4 Cognizant has provided little justification for these requests, which total 6.9 hours at a rate 5 of $646.00 per hour. By providing such bare and unhelpful explanations, Cognizant does not 6 carry its burden of showing how the fee request is reasonable. Accordingly, I will deduct one-half 7 of these fee requests, or $2,228.70. 8 B. Redacted Billing Descriptions 9 A number of fee requests redact the description of the work performed. As I have said in another case, a party "is not allowed to petition the Court for fees but hide from the public the 11 United States District Court Northern District of California 10 basis for its request." Muench Photography, Inc. v. Pearson Educ., Inc., No. 12-cv-1927, 2013 12 WL 6698465, at *2 (N.D. Cal. Dec. 18, 2013). Accordingly, I will deduct from the following 13 redacted entries the proportion of the fees relative to what I surmise to be the corresponding 14 portion of work described in the redacted entry, see Lota by Lota v. Home Depot U.S.A., Inc., No. 15 11-cv-5777-YGR, 2013 WL 6870006, at *12 (N.D. Cal. Dec. 31, 2013) ("it is within this Court's 16 discretion to make deductions for block-billing"): 17  third, or $511.70. 18 19     28 March 10, 2014 – Medzhibovsky: $1,690.00 for 2.6 hours, to be reduced by onequarter, or $422.50. 26 27 March 3, 2014 – Rodrigues: $493.43 for 0.9 hours, to be reduced by one-half, or $246.72. 24 25 March 3, 2014 – Medzhibovsky: $1,625.00 for 2.5 hours, to be reduced by onethird, or $541.66. 22 23 February 25, 2014 – Medzhibovsky: $2,210.00 for 3.4 hours, to be reduced by one-half, or $1,105.00. 20 21 February 21, 2014 – Rodrigues: $1,535.10 for 2.8 hours, to be reduced by one-  March 18, 2014 – Ganas: $2,297.13 for 4.7 hours, to be reduced by one-quarter, or $574.28. 5  1 $325.83. 2  3 March 19, 2014 – Rodrigues: $4,550.48 for 8.3 hours, to be reduced by one-third, or $1,516.83. 4  5 March 20, 2014 – Rodrigues: $2,028.53 for 3.7 hours, to be reduced by one-third, or $676.18. 6  7 March 21, 2014 – Rodrigues: $2,028.53 for 3.7 hours, to be reduced by one-half, or $1,014.27. 8  9 March 28, 2014 – Medzhibovsky: $1,560.00 for 2.4 hours, to be reduced by onehalf, or $780.00. 10  11 United States District Court Northern District of California March 19, 2014 – Ganas: $977.50 for 2 hours, to be reduced by one-third, or March 31, 2014 – Medzhibovsky: $780 for 1.2 hours, to be reduced by one-half, or $390.00. 12  13 March 31, 2014 – Rodrigues: $383.78 for 0.7 hours, to be reduced by one-half, or $191.89. 14 15  Completely redacted entry, Rodrigues Decl. Ex. B at 21, to be reduced by $750.00.1 16  Completely redacted entry, Rodrigues Decl. Ex. B at 27, to be reduced by $28.83. 17 The total amount to be deducted due to redacted entries is $9,075.69. 18 C. Unreasonable Billing Amounts 19 On March 20, 2014, paralegal Jeff Reeves billed 2.6 hours at a rate of $263.50 to draft an 20 application for the pro hac vice admission of two attorneys. Rodrigues Decl. Ex. B at 6. On April 21 2, 2014, the paralegal billed another 0.6 hours to "[r]evise" the applications. Rodrigues Decl. Ex. 22 B at 18. Pro hac vice applications of this Court are one-page documents in which nothing more is 23 requested other than the attorney's name, the client's name, the attorney's bar membership, local 24 counsel's name, and the address, phone number, and email address of the attorney and local 25 counsel. See Dkt. Nos. 21, 22. To bill $843.20 to fill out these forms is unreasonable. 26 27 1 28 Even the amount requested for the "completely redacted entries" are redacted, so the Court had to take the total amount requested for the relevant period and subtract all other disclosed amounts. 6 1 One attorney billed 0.4 hours at a rate of $548.25 to "[r]eview and execute" the 2 applications. Rodrigues Decl. Ex. B at 18. In other words, an attorney with six years of legal 3 experience spent 24 minutes to verify her contact information and sign her signature at a cost of 4 $219.30. See Rodrigues Decl. ¶ 11. This is unreasonable (and it is telling that the second attorney 5 who was admitted pro hac vice did not bill the time reviewing and executing his application). From the paralegal's billing request, I deduct 2.5 hours, or $658.75. From the attorney's 6 7 billing request, I deduct the entire $219.30 amount. 8 D. Other Fees 9 As I indicated above, a review of Cognizant's counsel's billing records suggests that certain tasks could have been performed more efficiently or would have been more cost- 11 United States District Court Northern District of California 10 effectively performed by a junior attorney or non-attorney. For example, Cognizant argues that it 12 "reasonably limited the time billed by its partners, who have the highest billing rate." Mot. 4. On 13 the contrary, one of the highest billers by far in terms of hours billed was a senior attorney whose 14 rate of $620.50 per hour is only slightly less than the billing rates of the partners assigned to the 15 case (i.e., $650.00 and $646.00). See, e.g., Rodrigues Decl. Ex. C at 3. Similarly, I am unsure 16 why counsel assigned associates to upload files to an FTP website rather than having a discovery 17 specialist or paralegal perform that task. In any event, "[i]t is not practical for me to discuss each of the remaining fee entries in the 18 19 detail I have addressed the fees discussed above." Hernandez v. Taqueria el Grullense, No. 12- 20 cv-3257-WHO, 2014 WL 1724356, at *15 (N.D. Cal. Apr. 30, 2014). The Ninth Circuit has said 21 that "the district court can impose a small reduction [on the requested fees], no greater than 10 22 percent—a 'haircut'—based on its exercise of discretion and without a more specific explanation." 23 Moreno v. City of Sacramento, 534 F.3d 1106, 1112 (9th Cir. 2008). I will exercise my discretion 24 to do so and will reduce the adjusted fees request by an additional 10 percent, from $138,784.65 to 25 $124,906.18. 26 III. 27 28 CALCULATION For the reasons detailed above, I find that $124,906.18 of the fees and $5,435.55 of the costs, totaling $130,341.73, requested in this matter were reasonable. Adjustment to this figure 7 1 based on the Kerr factors is not necessary because my consideration of the Kerr factors was 2 subsumed in the preceding analysis. See Secalt, 668 F.3d at 689. CONCLUSION 3 4 Cognizant's counsel did good work in this case and achieved the desired result for their 5 client. They charge premium rates that are justified by their education, experience, and the quality 6 of the work performed. They are entitled to their reasonable fees and costs. I have no doubt, too, 7 that the individuals for whom Cognizant requests fees performed the tasks described. But I have 8 an independent obligation to ensure that all fee requests are reasonable and sufficiently justified. 9 Because some of them were not, the reductions described in this Order are necessary. 10 Cognizant's motion for attorney's fees and costs is GRANTED in part and DENIED in United States District Court Northern District of California 11 part. McAfee shall pay Cognizant $124,906.18 in fees and $5,435.55 in costs, totaling 12 $130,341.73. The bond of $100.00 that Cognizant posted shall also be returned. 13 14 15 16 IT IS SO ORDERED. Dated: August 7, 2014 ______________________________________ WILLIAM H. ORRICK United States District Judge 17 18 19 20 21 22 23 24 25 26 27 28 8

redpajama_set_name: RedPajamaCommonCrawl


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South Africa 4-94 chasing 305 to win the test | Canberra weather
By Mark D. Quinto	 Last updated Dec 29, 2021
sport, cricket
India are well positioned to claim victory in the opening test as they look to win a series in South Africa for the first time. Tourists will need six wickets and South Africa 211 tracks, when play on the final day begins Thursday at Centurion Park in Pretoria in the first of three tests. After knocking out India for 174 in their second round midway through Matchday 4, South Africa found themselves chasing 305, a record goal at the venue, in four and a half sessions. They closed on 4-94 with Dean Elgar fighting 195 minutes for an unbeaten 52. India got an early breakthrough when Mohammed Shami, who took 5-44 in the opening innings, prompted Aiden Markram to play for a in the second. Keegan Petersen called for 17, caught by Mohammed Siraj. On a lively wicket providing plenty of help to the seamers, Elgar and Rassie van der Dussen held 22 overs, adding 40, before Jasprit Bumrah returned the ball to the bowl, the latter offering no shots for a 65-ball. 11. In the final day on Bumrah followed by yorking night watchman Keshav Maharaj (8) to end play. "The wicket has variable bounce, so if we keep playing in the right areas we are in good shape. position in the game, "said Indian batting coach Vikram Rathour. "If we can continue to do this tomorrow, I think we will create a lot of opportunities… We have to continue to achieve these goals consistently." "We have to show faith," said South African fast bowler Kagiso Rabada. "We'll strategize overnight and figure out how we want to approach this." Dean has done it countless times, where he shows the fight when it's hardest. He will know his job is not finished, he is leading forward. Earlier, Rabada took 4-42 as the quick Proteas bowlers grabbed the Indian ten wickets. Marco Jansen landed 4-55 and Lungi Ngidi picking up the other two Rishabh Pant wickets, with a run-a-ball 34, scored the best score with only KL Rahul (23) and Ajinkya Rahane (20). the day 1-16 and wickets lost at regular intervals. Nevertheless, they are likely to have made enough points. The highest fourth inning pursuit at Centurion Park was 8-251 by England in 2000, the infamous test where Hansie Cronje brokered a deal in which both teams lost a round after the rain to force a result. It was one of only two defeats for South Africa on this pitch. The next high is 4-226 by South Africa against Pakistan in 1998. But the weather could thwart India. The second day has leached out, and more rain is forecast for at least part of the fifth day. With Australian Associated Press agencies
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December 30, 2021 – 3:53 am
India are well positioned to claim victory in the opening test as they look to win a series in South Africa for the first time.
Tourists will need six wickets and South Africa 211 tracks, when play on the final day begins Thursday at Centurion Park in Pretoria in the first of three tests.
After knocking out India for 174 in their second round midway through Matchday 4, South Africa found themselves chasing 305, a record goal at the venue, in four and a half sessions.
They closed on 4-94 with Dean Elgar fighting 195 minutes for an unbeaten 52.
India quickly made a breakthrough when Mohammed Shami, who took 5-44 in the opening innings, prompted Aiden Markram to play for one in the second.
Keegan Petersen called for 17, caught by Mohammed Siraj.
On a lively wicket providing plenty of help to the sitters, Elgar and Rassie van der Dussen held 22 overs, adding 40, before Jasprit Bumrah returned the ball to the bowl, the latter offering no shots for a 65- ball 11.
In today's final against Bumrah, followed by York's night watchman Keshav Maharaj (8) to end the game.
"The wicket has variable rebound so if we keep playing in the right areas we are in a good position in the game," said Indian batting coach Vikram Rathour.
"If we can continue to do this tomorrow, I think we will create a lot of opportunities… We have to continue to achieve these goals consistently."
"We have to show faith," said South African fast bowler Kagiso Rabada. "We will strategize overnight and determine how we want to approach this.
"Dean has done it countless times, where he shows the fight when it's the hardest. He'll know his job isn't done, he's leading forward."
Earlier, Rabada took 4-42 as the Proteas' fast bowlers grabbed the Indian ten wickets. Marco Jansen landing 4-55 and Lungi Ngidi picking up the other two wickets.
Rishabh Pant, with a run-a-ball 34, had the best score with only KL Rahul (23) and Ajinkya Rahane (20) also coming out of their teens.
India, having established a 130-point lead in the first inning, started the day 1-16 and lost wickets at regular intervals. Nevertheless, they are likely to have done enough shopping.
The highest fourth inning chase at Centurion Park is 8-251 by England in 2000, the infamous test where Hansie Cronje brokered a deal in which both teams lost a round after the rain to force a result. . It was one of only two defeats for South Africa on this pitch.
The second highest is 4-226 by South Africa against Pakistan in 1998.
But time could thwart India. The second day was washed away and more rain is forecast for at least part of the fifth day.
Associated Australian Press
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Der Begriff Divergenzhypothese bedeutet, dass von der Annahme ausgegangen wird, zwei oder mehrere Sachverhalte würden sich im Laufe der Zeit zunehmend auseinanderentwickeln (vgl. Divergenz und Hypothese).

Wirtschaft
Der Begriff findet in der Wirtschaftswissenschaft Anwendung. Er bezeichnet dabei beispielsweise eine möglich künftige weitere Auseinanderentwicklung der Lebensverhältnisse in armen und reichen Regionen.

Pädagogik, Psychologie
Hier wird der Begriff "Divergenzhypothese" verwendet, eine asynchrone Entwicklung und damit das Auftreten von Defiziten in den Bereichen Persönlichkeitsentwicklung und Sozialverhalten bei Hochbegabten zu beschreiben. Gleichbedeutend werden hier "Licht-und-Schatten-Hypothese", sowie "Dysharmonie-Hypothese" verwendet.

Soziologie
In diesem Bereich beschreibt sie als Beispiel die im Rahmen der Globalisierung spekulativ zu erwartenden Veränderungen der Gesellschaftsformen (z. B. Kapitalismus).

Einzelnachweise

Differentielle und Persönlichkeitspsychologie
Pädagogik
Globalisierung
Volkswirtschaftslehre
Wissenschaftstheorie
Sozialer Wandel

redpajama_set_name: RedPajamaWikipedia


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Home » News » Ladbrokes Coral to pay £5.9m for social responsibility and AML failings
Ladbrokes Coral to pay £5.9m for social responsibility and AML failings
The GB Gambling Commission has handed Ladbrokes Coral a penalty package of £5.9m (€6.4m/$7.2m) for systematic failings related to social responsibility and anti-money laundering measures, while investigations into the actions of personal management licence-holders continue.
A Commission-led investigation found that from November 2014 to October 2017, both Ladbrokes and Coral failed to put in place effective safeguards to prevent money laundering and consumers suffering gambling harm.
The regulator noted that this applied to when Ladbrokes and Coral operated as separate entities prior to merging in November 2016, as well as after they joined together to form the Ladbrokes Coral Group, which is now owned by GVC Holdings.
The Commission, which said GVC fully complied with its investigation, focused on Ladbrokes Coral's handling of seven customers' accounts, having brought together complaints from legal representatives, reports from other agencies and associated media reports.
Among the specific failings highlighted by the Commission was an instance when Ladbrokes did not carry out any social responsibility interactions with a customer who lost £98,000 over two-and-a-half years, had 460 attempted deposits declined, and asked the operator to stop sending promotions.
Another customer spent £1.5m over the space of two years and 10 months, and although Coral did request to see evidence of their source of funds, the operator could not provide evidence of social responsibility interactions. This is despite the customer displaying signs of problem gambling, including logging into their account on an average of 10 times per day for a month and losing £64,000 in the process.
Ladbrokes could also not provide evidence of carrying out social responsibility interactions with a customer who deposited more than £140,000 in the first four months of their account being open.
In addition, the Commission highlighted how Ladbrokes identified concerns with a customer, but allowed further significant gambling without taking additional steps to verify the source of funds or consider if the customer in question could afford to spend and lose this amount of money.
The Commission ruled that Ladbrokes Coral was in continual breach of licence condition 12.1, which requires full compliance with the Money Laundering Regulations 2007, and the ordinary code provision that preceded this condition before being replaced with the updated version in October 2016.
Licence condition 12.1.1(1) requires: licensees to conduct an assessment of the risks of their business being used for money laundering and terrorist financing.
The regulator also found Ladbrokes Coral in breach of social responsibility code provision 3.4.1, which requires effective policies and procedures for customer interaction. This includes a requirement to make use of all relevant sources of information, to identify at-risk customers who may not be displaying obvious signs and to interact with VIP players.
GVC and Ladbrokes Coral have admitted to the failings and agreed to pay the penalty package in full. A payment of £4.8m will be made in lieu of a financial penalty, which will be directed towards delivering the National Strategy to Reduce Gambling Harms.
A total of £1.1m will be paid out to victims where it has been found, or could reasonably be suspected to be, the proceeds of crime. GVC will also pay £24,700 towards the Commission's costs of investigating the case.
GVC has also committed to review five further customer accounts identified by the Commission and will divest itself of any gross gambling yield as directed.
"Decision makers at gambling businesses need to invest in the welfare of their customers and the integrity of money being gambled with," the Commission's executive director, Richard Watson, said.
"These were systemic failings at a large operator which resulted in consumers being harmed and stolen money flowing though the business and this is unacceptable."
In addition to agreeing to pay the fine, GVC has committed to overhauling its responsible gaming and customer interaction processes, including increases in resources, staff retraining and hiring a dedicated player protection expert outbound call team.
GVC will also implement its 'Changing for the Bettor' strategy, comprising research and educational projects, funding treatment for problem gambling, creating cultural change and promoting responsible attitudes in the industry.
Further planned activity includes engaging a UK firm of solicitors to review any new high or higher-risk customers as may be identified by the Commission or by GVC, with any findings to be fed back into improvements that could be made to current processes and dealing with divestment.
The solicitors' firm will also undertake a review and dip-sample of an internal review completed by Ladbrokes Coral from July to October 2017, applying its new processes to all active customer accounts to evaluate whether it was robust and fit for purpose. GVC will then instruct the firm to dip-sample an internal review of a group of customers, to evaluate the robustness of this process.
The appointed firm will manage and oversee a review of the current Ladbrokes Coral process and provide an independent analysis of its procedures to ensure it meets or exceeds its regulatory obligations.
In addition, the solicitors will review the top 50 customers by gross gambling yield (GGY) for the years 2015, 2016 and 2017 to consider whether any of the failings identified in the Commission's report are evidenced and if so, to divest GGY accordingly.
Commenting on the ruling, GVC chief executive Kenneth Alexander said: "Soon after the acquisition of Ladbrokes Coral following meetings and ongoing enquiries by the Gambling Commission, it became clear to GVC that there had been historic compliance failures within certain areas of the operations.
"Working closely with the Gambling Commission and an independent firm of solicitors, GVC facilitated a thorough, prompt and far-reaching investigation, which has led to today's settlement.
"These historical failings were unacceptable and since the acquisition, I have overseen a systematic review of the enlarged group's player protection procedures and the individuals responsible for these problems have exited the business. I am confident that, we now have in place a robust and industry leading approach to player protection.
"More broadly, GVC is determined to take the lead in the critical area of responsible gambling, and is taking decisive, tangible action across a range of initiatives.
"However, there is more to be done and social responsibility and we will continue to work with other gambling companies and the Gambling Commission to raise operating standards."
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Showing results by author "Alfred Tennyson"
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Unabridged (32)
The Poet Laureates - Volume 2
Written by: William Wordsworth, Alfred Lord Tennyson, Alfred Austin
Narrated by: David Shaw-Parker, Richard Mitchley, Ghizela Rowe
The office of Poet Laureate is a high honour amongst poets. The ancient Greeks had the first idea, and their heroes and poets wore wreaths of laurel in honour of the god Apollo. Many countries now have a laureate, as do many societies and organisations. But perhaps ranked first among them all is that of our own Poet Laureate. Unfortunately no single authentic definitive record exists of the office of Poet Laureate of England. In some form it can be traced back to 1189 and Richard Canonicus, who was employed by Richard I with the title 'versificator Regis'.
Price: CDN$ 6.13
The Great Poets: Alfred Lord Tennyson
Written by: Alfred Tennyson
Narrated by: Michael Pennington
Length: 1 hr and 6 mins
The 200th anniversary of the birth of Alfred, Lord Tennyson (1809 - 1892), one of the most popular of poets, is celebrated in 2009. Works such as The Charge of the Light Brigade, Crossing the Bar and Tears, Idle Tears have made him an internationally famous figure, and the second most quoted writer of all time (after Shakespeare).
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Collection: Popular Poetry / Popular Verse, Vol. 2
Written by: William Blake, John Donne, Alfred Tennyson, and others
Narrated by: Jasper Britton, Emma Fielding, Tony Britton
Nearly 100 of the most popular and loved poems in the English language, this collection is one of the most comprehensive anthologies of its kind available. It covers a remarkable range, from the striking vision of Blake and Shelley and the insights of Keats to lighter but equally memorable verse by Tennyson, Donne, and Edward Lear.
Written by: William Blake, John Donne, Alfred Tennyson, Edward Lear, John Keats
Idylls of the King
Narrated by: Charlton Griffin
The Arthurian legend of Camelot has been told many times, but never better than by Alfred Tennyson. Employing some of the most stirring and beautiful blank verse ever written, Tennyson crafted his version of the Knights of the Round Table over the course of nearly fifty years, completing it in 1885. Despite the length of time, Tennyson managed to maintain a high level of style and continuity throughout.
Canto 27 from In Memoriam AAH
Written by: Alfred Lord Tennyson
Narrated by: Mike Vendetti
Read by award-winning narrator Mike Vendetti. "Tis better to have loved and lost, than never to have loved at all." Comes from this poem.
The Poetry of Morning
Written by: D. H. Lawrence, Alfred Lord Tennyson, Robert Louis Stevenson
Narrated by: Richard Mitchley, Ghizela Rowe, Gideon Wagner
Over the far horizon the blanket of night begins to slowly dissolve. The sun is once more on its daily journey across the heavens. The light begins to sharpen and increase in intensity, revealing the landscape. Morning has begun, and dazed heads and sleepy faces come to terms with the new day. Our poets capture the mood, the emotions and all manner of other details in their descriptions of this time. But then with the calibre of wordsmiths such as Tennyson, Wordsworth, Milton, Southey, Donne and many more besides, we are almost spoilt.
Poetic Christmas: Beloved Holiday Poems
Written by: Louisa May Alcott, Emily Dickinson, E. E. Cummings, and others
Narrated by: Sheryl Mebane
Length: 15 mins
Enjoy these 10 Christmas pieces by celebrated authors. The experience includes music and a range of lively and touching characters. Add a little poetry to your Christmas!
Written by: Louisa May Alcott, Emily Dickinson, E. E. Cummings, Henry Wadsworth Longfellow, Clement Clarke Moore, Marjorie L. C. Pickthall, Christina Rossetti, William Shakespeare, Alfred Tennyson
Ring Out, Wild Bells
Musically Inspired Christmas Poems
Written by: Louisa May Alcott, William Shakespeare, Alfred Tennyson, and others
Length: 4 mins
These holiday poems by celebrated authors are presented musically in fun, exciting, and stirring ways. Sing and play along with loved ones or just sit back and let the experience transport you!
Written by: Louisa May Alcott, William Shakespeare, Alfred Tennyson, Sheryl Mebane
Narrated by: David McCallion
This series of poems covers the story of the legendary hero, King Arthur, beginning with his first encounter with Guinevere, the woman who would become his queen on his search for the Holy Grail, to the betrayal of Guinevere and Sir Lancelot, and finally ending with Arthur's last battle. First published between 1859 and 1885 as a series of twelve poems, Idylls of the King retells the story of King Arthur with a unique and Victorian flavor beloved by many.
Award-winning narrator Mike Vendetti performs Tennyson's oft quoted poem Ulysses, a work that has withstood the test of time.
The Poetry Hour, Volume 7
Time for the Soul
Written by: Alfred Lord Tennyson, Ella Wheeler Wilcox
Narrated by: Richard Mitchley, Ghizela Rowe
Length: 1 hr and 1 min
Poetry is often cited as our greatest use of words. The English language has well over a million of them and poets down the ages seem, at times, to make use of every single one. But often they use them in simple ways to describe anything and everything from landscapes to all aspects of the human condition. Poems can evoke within us an individual response that takes us by surprise, that opens our ears and eyes to very personal feelings.
A Quartet of Tennyson
Enoch Arden, Guinevere, Marianna, The Kraken
Narrated by: Helen Elizabeth G
Alfred Tennyson, 1st Baron Tennyson (6 August 1809 - 6 October 1892) was Poet Laureate of the United Kingdom and remains one of the most popular poets in the English language. He was born in Somersby, Lincolnshire, a rector's son, the fourth of 12 children, and reportedly a descendant of King Edward III of England.
Narrative Verse, Volume 3
Written by: Christina Rossetti, Henry Longfellow, Edgar Allan Poe, and others
Narrated by: Sean Barrett, David Shaw-Parker
Poetry can capture the imagination in a few short lines but narrative verse or poetry takes the form of telling a story, whether it be simple or complex in a longer form. Among the most ancient forms of poetry, it has widespread roots through almost every culture. In Volume 3 we bring you the classics 'Goblin Market' by Christina Rosseti; 'The Wreck of the Hesperus' by Henry Wadsworth Longfellow; 'The Raven' by Edgar Allan Poe; 'Morte D'Arthur' by Alfred Lord Tennyson; and from 'Horatius' by Thomas Babington Maculay.
Written by: Christina Rossetti, Henry Longfellow, Edgar Allan Poe, Alfred Tennyson, Thomas Maculay
A Grief at Christmas
Narrated by: Glenn Hascall
A classic poem from acclaimed author Alfred, Lord Tennyson. Grief sometimes comes at Christmas. We may believe there is no hope for happiness again on the day of Christmas bells and gifts, but in the midst of this grief there is the birth of hope. When something is lost - something new may be found. Not easy, but universally true.
Maud (BBC Radio 4: Classic Serial)
Narrated by: Joseph Millson, Katheryn Nutbeem
A disturbed young man roams the windswept hills, haunted by his father's suicide and his mother's early death. He blames his father's old friend, the lord of the Hall, for his ruin. The young man was betrothed to Maud, the lord's daughter, when they were children, but she and her family left the area after the suicide. But now there are workmen up at the Hall - Maud has come home.
The Sea - An Element in Verse: Volume 2
Written by: Alfred Lord Tennyson, Algernon Charles Swinburne, John Keats, and others
Narrated by: Gideon Wagner, Ghizela Rowe
The seas and oceans have a mystical power over us: From a playful day at the beach to the hysterical waves of a storm, this ever-changing element evokes both beauty and fear. Its great mass, its shimmering beauty, its raging howl, and all in colours from blue to grey to green and crystal clear. In these collections of verse our poets - including Tennyson, Swinburne, Keats, Shelley, and many others - explore the relationship between ourselves and the great mystical waters.
Written by: Alfred Lord Tennyson, Algernon Charles Swinburne, John Keats, Percy Bysshe Shelley
Enoch Arden
Melodrama for Speaker and Piano
Written by: Alfred Lord Tennyson, Richard Strauss (music)
Narrated by: Benjamin Luxon, Frederick Moyer (piano)
Enoch Arden first came to international attention with a recording by Claude Raines and Glenn Gould, but it has since drifted back to obscurity. This is a work that both Luxon and Moyer have loved for many years. The poem is immediately accessible to any audience and tells a heart-wrenching story of friendship, love, separation, and sacrifice. The masterful score creates a powerful soundtrack to the saga.
Written by: Alfred Tennyson, Richard Strauss (composer)
Continuing a collaboration started years ago, Benjamin Luxon and Frederick Moyer now turn to the little-explored genre of music for piano and narrator. Enoch Arden first came to international attention with a recording by Claude Raines and Glenn Gould but has since drifted back to obscurity. This is a work that both Luxon and Moyer have loved for many years. The poem is immediately accessible to any audience and tells a heart-wrenching story of friendship, love, separation, and sacrifice.
The Classical Poetry Collection, Volume 4
Written by: Thomas Hardy, Rupert Brooke, William Blake, and others
Narrated by: Richard Burton, Dylan Thomas, Edith Evans
The finest voices reading a wonderful selection of poetry accompanied by selected classical music.
Written by: Thomas Hardy, Rupert Brooke, William Blake, Alfred Tennyson, A. E. Houseman
The Poetry of December
A Month in Verse
Written by: John Keats, Percy Bysshe Shelley, Alfred Tennyson, and others
December - the 12th and closing month in the Gregorian calendar. Winter is upon the land, and the poets, including such as Keats, Shelley, Tennyson, Shakespeare, and Stevenson, share their views and thoughts.
Written by: John Keats, Percy Bysshe Shelley, Alfred Tennyson, William Shakespeare, Robert Louis Stevenson
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Yesterday, The Center for Political Accountability announced that Chair of the Patriotic Millionaires Morris Pearl has joined their Board of Directors. Pearl brings career experience and a commitment to reforming the influence of money in politics to this already established board.
Corporate political spending without accountability does not benefit the company or the shareholders. Pearl will continue to work with both the Patriotic Millionaires and The Center for Political Accountability to ensure fair political practices for all Americans.


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Symposium Papers
Submissions Information
Undergraduate Journal of Art History & Visual Culture
2018 Symposium Papers
The Offender Behind the Lens: The Enduring Ethical Legacy of Beitler's Lynching Photograph
July 14, 2018 UJAH
By Jeffrey Tse
Racial prejudice in the 1930s is a widely explored topic in terms of the motivational factors behind the oppression of African Americans. One theoretical standpoint suggests that the racial tensions between black and white citizens increased due to the economic stressors experienced during the Great Depression[1]. Nevertheless, American history has shown that racism and oppression experienced by the African American community was also codified into US law, bearing a multitude of ramifications on the social rights, and often, the lives of African Americans. Furthermore, racial prejudice experienced by African Americans deprived many of their lives, as history has made evident during the Slave Trade, but also through contemporary activist movements, such as Black Lives Matter. The attitudes during the 1930s encompassed intense violence towards the African American community, a situation largely accepted by white citizens, and even reveled in. The Jim Crow era, originating in 1877, was a particularly brutal time for African Americans, which saw the murder of many innocent black people with little cause, often relating to the single fact of difference. The denigration and humiliating depictions of lynched men were captured in photographs, which also included the poses of proud white supremacists. White photographers at the time of the Great Depression are commonly thought to have sympathized with these white supremacists, ensuring that their presence during a lynching was accepted. The social responsibility of photojournalism and the role of this profession in perpetuating racism in the US has frequently come under scrutiny. The manners in which these photojournalists have captured historically shameful moments in the past are also known to have contributed to the social attitudes in the country. As abovementioned, this attitude, codified into US law, still persists in modern American society. One such photographer was Lawrence Beitler, who appears to have had foreknowledge of an upcoming lynching and prepared his tripod to capture these murders. It is often debated whether Beitler's photography of these murders was a result of the non-interference approach in photojournalism, however, it is suggested that photojournalists in the 1930s often adopted complacency towards the violence that they documented. Beitler further developed these images for sale in the form of postcards, indicating that the lynchings were an acceptable and profitable practice. This study, therefore, analyzes the extent to which photographers contributed to the desensitization of white society to repeat lynchings inflicted on African Americans, and how these recorded images further devalued the lives of the victims. Furthermore, I will discuss how the distribution of these images thereafter allowed for such levels of violence to be seen as commonly acceptable during the Great Depression: ultimately contributing to the mistreatment of African Americans in the periods which followed, for instance, the Civil Rights Movement. In analyzing the role of photojournalism contributing to the racial prejudice experienced by African Americans, I will critique the field of photojournalism in terms of professional ethics and complacency.
[1] Julius E. Thompson, Lynchings in Mississippi: A history, 1865-1965, (Jefferson, McFarland and Company, Inc., 2007), 114.
Content warning: Please note that the PDF below contains graphic imagery.
Click here to download the full paper
tags 2018 Symposium
The Tartan Ladies: A Comparative Analysis of Tartan and Gender through Queen Victoria and the Scottish Suffragettes


Having visited only three of the top ten happiest countries on earth, clearly I have a lot of work to do.
After finally visiting the original Dover Street Market in London, the stateside version does not disappoint, especially with this week's sale!
Most epic road trips begin with a glancing view from the BQE of the Brooklyn Bridge Park and the thought that I need to go there more. With this interactive art display from Danish artist Jeppe Hein, I have no excuse.
On book 2 of The Southern Reach Trilogy by Jeff Vandermeer and can not put my Kindle down. The books are major page turners filled with lush, otherwordly details.
"I've been laughed at in meetings" and other honest moments from designer Rachel Roy's viewpoint at the helm of a powerhouse brand.
Have a minor obsession happening with this pure, organic, locally made moisturizer. I slather it on my nails, my feet, my elbows, anywhere that feels extra parched. And it with its lavender scent, each use is like a mini spa treatment.


Blue Planet Network - About Blue Planet Network: Our mission is to exponentially increase the impact of safe drinking water programs for people around the world.
Our mission is to exponentially increase the impact of safe drinking water programs for people around the world.
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110 organizations working on water and sanitation access in 27 countries use our services to improve their impacts.
1,950 member water and sanitation projects, totaling $45 million, are tracked and managed on Blue Planet Network.
Thrive Networks delivers innovative solutions to difficult development problems faced by poor families and communities around the globe. Since 1988, more than 5.9 million impoverished individuals have benefited from Thrive Network's high-impact, results-oriented programs in health, clean water and sanitation, and education. The organization has invested over $106 million in development solutions in Asia—where it operates programs in Vietnam, Cambodia, India, Laos, Myanmar, Philippines and Timor-Leste—and has launched programs in West Africa.
Since our founding in 2002, it has been Blue Planet Network's ambitious goal to ensure that 200 million people in need gain access to safe drinking water. But gaining access to water is just the first step. Keeping it is as important.
In its early years, Blue Planet Network worked to build awareness and funds for water projects through epic undertakings. Blue Planet Run 2007, the first global relay run for safe drinking water, and Blue Planet Run: The Race To Provide Safe Drinking Water To The World, a powerful book that tells the human story of water through photos and essays, connected people around the world to the water crisis and what they could do to solve it.
Along the way, however, we realized that all the water crisis awareness in the world wouldn't help if people couldn't easily find great implementing organizations and water project plans, and be able to easily track the impact of their support. Likewise, the experience of those capable implementers would be wasted if they didn't have a way to continuously improve through learning best practices and sharing their work with the world.
We saw that we could add real value to the fight for clean water by creating a scalable platform to 1) connect water project funders and implementers to create new, effective partnerships; and 2) manage the planning, funding, implementation and tracking of tens of thousands of water and sanitation projects for greater impact. We always work to be catalysts for positive change across the entire water and sanitation sector.
We launched Peer Water Exchange, our original online technology platform, in 2006 with five member organizations. This has grown into a vibrant community delivering real improvements to water and sanitation programs and projects around the world.
We changed our name to Blue Planet Network in 2010 to emphasize our mission and to welcome funders, as well as implementers, as members to help us expand our reach and collective impact.
Blue Planet Network and Thrive Networks merged on September 6, 2013, bringing together Thrive Networks' market-leading "pay for performance" water and sanitation programs (WASH) and Blue Planet Network's unique online collaboration and impact analysis platform. The merger will accelerate innovation across the sector, drive learning and visibility, and deliver improved clean water and sanitation solutions to more people around the globe. Blue Planet Network is now a program of Thrive Networks. Blue Planet Network continues to operate and grow its online collaboration platform and network of 100+ expert WASH organizations. Blue Planet Network will retain its name and remain an open community and platform driven by its members' needs.
Get in-depth information about Blue Planet Network on Guide Star.


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\section{Introduction}

The unique properties of graphene, the first truly two-dimensional material, have spurred a flood of research on fundamental physics and on technological possibilities. \cite{Neto_Gfn_ElProp_RMP09, Castro_BBLG_ElProp_JPCM10, Nilsson_BLG_MultiLG_electron_PRB08, SDS_Gfn_RMP11, PesinAHM_Gfn_Spintron_NP12, McCann_MLGBLG_ElProp_12, McCann_BLG_ElProp_12} Monolayer graphene (MLG) has a non-Bravais honeycomb lattice structure with two triangular sublattices.  The physical consequences of its linear
$\pi$-band crossing at the Fermi level, described at low energies
by a chiral massless Dirac $\vec{k} \cdot \vec{p}$ Hamiltonian, have been discussed at length.
Bilayer graphene (BLG) consists of two Bernal-stacked coupled graphene monolayers, resulting in four inequivalent sites and four corresponding $\pi$-bands.  Its carriers are chiral but massive and characterized
at low energies by a gapless parabolic spectrum displaying sublattice pseudospin-momentum locking.
In BLG a band gap may be induced by a top gate \cite{Oostinga_BLG_GateInducedInsul_NM08, KuzmenkoCrassee_BLG_TuneGap_PRB09, Deshpande_BLG_DiracPt_APL09} or by dual gates
which can vary the carrier density in the two layers independently. \cite{Ohta_BLG_ControlElStr_S06}
The theory of electronic transport in this unique and tunable $\pi$-band system has been investigated extensively. \cite{Adam_BLG_Transp_PRB08, Adam_BLG_TempDepCond_PRB10, SDS_BLG_Transp_PBR10, Culcer_BLG_transp_PRB09, Hwang_BLG_inhomogeneity_temperature_PRB10, Kechedzhi_BLG_TrigWarp_PRL07, Kechedzhi_MLG_BLG_WL_EPJ07, Koshino_BLG_Deloc_PRB08, KoshinoAndo_BLG_Transp_PRB06, Min_BLG_Opt_TranspGap_PRB11, Min_MultiLG_OptCond_PRL09, Rossi_BLG_Percol_PRL11, Sinner_MLG_BLG_Dis_Cond_PRB11, Trushin_BLG_ThermCond_EPL12, Trushin_BLG_MinCond_PRB10, Cserti_BLG_MinCond_TrigWarp_PRL07, Gradinar_BLG_Strain_Lifshitz_PRB12, Li_MLG_BLG_CrgImp_SSC12, Li_BLG_insulating_subgap_conductance_NP11, Prada_BLG_QSHE_SSC11, Yuan_BLG_TLG_DisTransp_PRB10, Hatami_BLG_MgnFldCondDis_PRB11, McCannFalko_BLG_LL_QHE_PRL06, Abergel_BLG_Vly_Crnt_APL09}
Experimental studies have focused on transport,
\cite{MiyazakiLi_BLG_unipolar_APL12, Miyazaki_BLG_Dis_PerpE_NL10, Bao_BLG_MinCond_12, Efetov_BLG_MultibandTransp_PRB11, Gorbachev_BLG_WL_PRL07, Lee_BLG_magnetotransport_NL11, Shioya_BLG_TuneNonlnrCrnt_APL12, VelascoJing_BLG_insulating_spectroscopy_NN12, Xiao_BLG_CrgImpSct_PRB10} magnetotransport, \cite{Novoselov_BLG_QHE_NP06, Henriksen_BLG_CycloRes_PRL08, Kim_BLG_SP_VP_PRL11, Sanchez-Yamagishi_BLG_Twist_QHE_PRL12, vanElferen_BLG_suspended_QHFmg_PRB12, Freitag_BLG_Susp_SpontGap_PRL12} and optics. \cite{Yang_MLG_BLG_Xtn_OptResp_PRL09, ParkLouie_Xtn_NL10, Martin_BLG_Susp_Compress_PRL10}  Recent efforts that have succeeded in manufacturing and manipulating quantum dots, \cite{Fringes_BLG_QD_PSSB11, Drocher_BLG_QD_12}  have been motivated by
potential applications in quantum computing.

An extensive body of research has been devoted to electron-electron interactions in BLG. \cite{Barlas_BLG_neutral_nonfermi_PRB09, NandkishoreLevitov_BLG_ee_PRB10, Lemonik_BLG_GS_PRB12, Nilsson_BLG_ee_PhaseDia_PRB06,
Stauber_BLG_Fmg_JPCM08, Jung_BLG_persistent_11, Jung_BLG_PseudospinFmg_PRB11, NandkishoreLevitov_BLG_QAHE_PRB10, Min_BLG_Superfl_PRB08, Zhang_BLG_SpontSymBrk_PRB10, Zhang_BLG_SpontQHE_PRL12, Barlas_BLG_exciton_condensation_PRL10, Castro_BLG_Fmg_PRL08, Mayorov_BLG_interaction_spectrum_S11, Abergel_BLG_Correl_10, KusminskiyCampbell_BLG_ee_EPL09, KusminskiyNilsson_BLG_Compress_PRL08, Borghi_BLG_Compress_PRB10, BorghiPolini_MLGBLG_Fermi_enhancement_SSC09, Sensarma_BLG_Correl_PRB11, Vafek_BLG_ee_RG_PRB10, Killi_BBLG_LuttLiq_PRL10,
Borghi_BLG_dynamical_response_collective_PRB09, Hwang_BLG_RKKY_PRL08, Wang_BLG_Scrn_PRB07, Tse_BLG_Drude_Scrn_PRB09, Sensarma_BLG_DynScrn_PRB10, Wang_BBLG_BBLG_PRB10, NandkishoreLevitov_BLG_DynScrn_Xtn_PRL10, Gamayun_BLG_DynScrn_PRB11, TriolaRossi_BLG_Gap_Scrn_12, Abergel_BLG_Gap_Screen_12, LvWan_BLG_screening_transp_PRB10, Bena_MLG_BLG_LDOS_1Imp_PRL08, Hwang_MLG_BLG_Drag_PRB11, Rossi_Gfn_EffMed_PRB09, Hassan_BLG_pn_plasmon_PRB12} Interactions in all forms of graphene are expected to be strong when the two-dimensional
material is surrounded by low-$\kappa$ dielectrics.
Progress in studying interaction effects has been
improved by achieving samples with higher mobility, \cite{Morozov_MLG_BLG_IntrMob_PRL08}
by studying suspended BLG samples that are not influenced by a substrate \cite{Feldman_BLG_Susp_BrkSym_NP09} and by breakthroughs in fabricating samples with top and back gates. \cite{Taychatanapat_BLG_DualGate_PRL10, Yan_BLG_Bolo_NN12} Interactions are expected to become more important as one approaches the charge neutrality point. \cite{Barlas_BLG_neutral_nonfermi_PRB09, NandkishoreLevitov_BLG_ee_PRB10}  In equilibrium interactions in BLG lead to competing ground states, \cite{Lemonik_BLG_GS_PRB12, Nilsson_BLG_ee_PhaseDia_PRB06} including a host of exotic states. \cite{Stauber_BLG_Fmg_JPCM08, Castro_BLG_Fmg_PRL08, Barlas_BLG_exciton_condensation_PRL10, Jung_BLG_persistent_11, Jung_BLG_PseudospinFmg_PRB11, NandkishoreLevitov_BLG_QAHE_PRB10, Min_BLG_Superfl_PRB08, Zhang_BLG_SpontSymBrk_PRB10, Zhang_BLG_SpontQHE_PRL12,Mayorov_BLG_interaction_spectrum_S11}
Theoretical studies of electron-electron interactions in equilibrium BLG\cite{KusminskiyNilsson_BLG_Compress_PRL08, Borghi_BLG_Compress_PRB10, BorghiPolini_MLGBLG_Fermi_enhancement_SSC09, Sensarma_BLG_Correl_PRB11, KusminskiyCampbell_BLG_ee_EPL09, Abergel_BLG_Correl_10, Vafek_BLG_ee_RG_PRB10, Killi_BBLG_LuttLiq_PRL10}
have demonstrated, among other properties, that screening and Friedel oscillations have different functional forms from MLG and 2DEGs. \cite{Hwang_BLG_RKKY_PRL08, Wang_BLG_Scrn_PRB07, Tse_BLG_Drude_Scrn_PRB09, Sensarma_BLG_DynScrn_PRB10, Wang_BBLG_BBLG_PRB10, NandkishoreLevitov_BLG_DynScrn_Xtn_PRL10, Gamayun_BLG_DynScrn_PRB11, TriolaRossi_BLG_Gap_Scrn_12, Abergel_BLG_Gap_Screen_12, Borghi_BLG_dynamical_response_collective_PRB09, LvWan_BLG_screening_transp_PRB10, Bena_MLG_BLG_LDOS_1Imp_PRL08}

The role of electron-electron interactions out of equilibrium has not yet received
attention. Given the wealth of research on transport, it is timely to address the influence
of electron-electron interactions on the charge conductivity of BLG.
As in single-layer graphene, charge currents in BLG lead to a net
pseudospin polarization.  Interactions are
therefore expected to renormalize the charge current and with it the pseudospin polarization.
The question naturally arises of whether this polarization may be enhanced by interactions
and produce observable effects.  It is important to understand whether the effect on the conductivity of non-equilibrium contributions to the interaction self-energy can be substantial, and whether it can be controlled using various tuning parameters such as the carrier density $n_e$.

This paper is therefore concerned with the effect of electron-electron interactions in bilayer graphene transport in the metallic regime $\varepsilon_F \tau/\hbar \gg 1$. We begin with the quantum Liouville equation for the density matrix, working in the first Born approximation with respect to momentum scattering.
Electron-electron interactions are taken into account self-consistently using the
non-equilibrium Hartree-Fock approximation, with screening treated in the random phase approximation.
We determine an exact expression for the conductivity in the presence of interactions within our framework. This work is distinct from recent papers discussing other interactions in BLG transport. \cite{Hassan_BLG_pn_plasmon_PRB12, Rossi_Gfn_EffMed_PRB09, Hwang_MLG_BLG_Drag_PRB11} In addition, the mean-field effect discussed here is not related to Coulomb drag, and electron-electron scattering is not relevant to the discussion at hand, which
for simplicity assumes that the temperature $T = 0$.

We demonstrate that electron-electron interactions renormalize
the charge conductivity. The interaction effect reduces
the conductivity.  However, the effect has a very weak density dependence and
will be difficult to distinguish experimentally from a slight increase in disorder strength,
which is not normally known.
Surprisingly, the interaction effect \textit{vanishes} as the carrier density $n_e$ tends towards zero
because of a subtle interplay between
the electric field, the pseudospin degree of freedom, and the electron-electron interactions
mean-field.   The effect is unexpectedly weak when the the Fermi wave vector $k_F$ is small compared to a wave vector $q_0$, introduced below, the size of which is set by the interlayer tunneling.
In BLG this wave vector is $q_0 \approx 4$nm$^{-1}$.  Consequently even a density $\sim 10^{13}$cm$^{-2}$,
which is relatively large in experimental terms, gives a Fermi wave vector small compared to $q_0$.

A recent study of out-of-equilibrium interactions in TI showed that, for a Dirac cone, the renormalized conductivity has the same density dependence as the bare conductivity.\cite{Culcer_TI_ee_PRB11} This result is expected to apply also to MLG. In BLG, however, one would expect the renormalization to have a different density dependence given the quadratic dispersion and different functional form of the screened Coulomb potential. We find that the density dependence of the renormalization is indeed different from that of the bare conductivity, but the fractional change in the conductivity due to interactions is much weaker than in TI/MLG and vanishes at low densities.
The vanishing of the renormalization in the limit $n_e \rightarrow 0$ is explained by the fact that the pseudospin of BLG is characterized by a winding number of 2. The projection of the equilibrium
pseudospin at ${\bm k}$ onto the pseudospin at ${\bm k}'$ has a different rotational symmetry than
the driving term due to the electric field.
As $n_e \rightarrow 0$, the product of these terms averages to zero over the Fermi surface.
In this sense the relative weakness of this interaction effect in BLG is
related to the smaller Fermi velocity enhancement in BLG compared to MLG. \cite{BorghiPolini_MLGBLG_Fermi_enhancement_SSC09}

The outline of this paper is as follows. In Sec.~\ref{sec:Ham}, we introduce the BLG band Hamiltonian and discuss the technical details of the kinetic equation solution.  In Sec.~\ref{sec:sct}, we calculate the scattering term in BLG in the Born approximation. In Sec.~\ref{sec:nonint} we briefly review charge transport in the absence of interactions. In Sec.~\ref{sec:int} we calculate the first order mean-field correction to the conductivity due to electron-electron interactions, then obtain an exact result to all orders. The results are discussed in Sec.~\ref{sec:disc}, while Sec.~\ref{sec:sum} summarizes our findings.

\section{Hamiltonian and Method}
\label{sec:Ham}

Our study is based on a commonly used $2$-band model for BLG:
\begin{equation}\label{BLGHamiltonian}
    H_{0{\bm k}} = Ak^2 \left(
    \begin{array}{cccc}
        0 & e^{-2i\theta} \\
        e^{2i\theta} &0\\
    \end{array}
    \right)
    =Ak^2({\bm \sigma}\cdot\hat{\bm n}_{\bm k})
\end{equation}
where $\hat{\bm n}_{\bm k}$ is the unit vector $(\cos2\theta,\sin2\theta)^{\mathrm{T}}$ with $\theta$ the polar angle of ${\bm k}$ and $A = \hbar^2v_F^2/t_\perp$ is a material-specific constant, which determines the Fermi velocity of BLG. Here $v_F$ is the (constant) Fermi velocity of MLG and $t_\perp \approx 0.4$eV is the interlayer hopping parameter.
\cite{SDS_Gfn_RMP11}
This model is valid at energies small compared to $t_\perp$, except that it
neglects trigonal warping terms which become important at very low energies.
(We comment on the role of these terms in Sec.~\ref{sec:disc}.)
It acts in a layer pseudospin space and has eigenstates which are equal weight sums of top and
bottom layers with interlayer phase angle $ 2 \theta$.
The Hamiltonian $H_{0{\bm k}}$ can be understood as representing a Zeeman-like interaction involving the pseudospin degree of freedom with a momentum-dependent effective magnetic field whose direction is given by
$\hat{\bm n}_{\bm k}$. Unlike MLG, the pseudospin winds twice when
momentum winds around the Fermi surface.
The eigenvalues of $H_{0{\bm k}}$ are $\varepsilon_{{\bm k}\pm} = \pm Ak^2$.

The many-body Hamiltonian $\mathcal{H}$ in $2^{nd}$ quantization is
\begin{equation}
    \arraycolsep 0.3 ex\begin{array}{rl}
    \displaystyle \mathcal{H} = & \displaystyle  \sum_{{\bm k}{\bm k}'ss'} (H_{{\bm k}{\bm k}'}^{ss'} c^\dag_{{\bm k}s} c_{{\bm k}'s'} +  \frac{1}{2} \, \sum_{\bm q} V_{\bm q} \, c^\dag_{{\bm k} + {\bm q}, s}c^\dag_{{\bm k}' - {\bm q}, s'}c_{{\bm k}'s'}c_{{\bm k}s}).
    \end{array}
\end{equation}
The one-particle matrix element $H_{{\bm k}{\bm k}'ss'}$ accounts for band structure contributions, as well as disorder and driving electric fields, discussed below.  For the matrix element $V_{\bm q} = V_{q}$
we use the statically screened Coulomb potential, determined here in the random phase approximation (RPA), \cite{Hwang_BLG_RKKY_PRL08} with $\epsilon_r$ the relative permittivity,
\begin{equation}
    V_q=\frac{e^2}{2\epsilon_0\epsilon_r[q + q_0g(q)]},
\end{equation}
where the constant wave vector $\displaystyle q_0=\frac{e^2}{2\pi\epsilon_0\epsilon_rA}$, and
\begin{equation}
    g(q)=\frac{1}{2k_F^2}\sqrt{4k_F^4+q^4}-\ln\bigg[\frac{k_F^2+\sqrt{k_F^4+q^4/4}}{2k_F^2}\bigg].
\end{equation}
$g(q)$ is a dimensionless function that increases monotonically from 1 to 1.755 as $q$ varies from 0 to $2k_F$, and the Fermi wave vector $k_F=\sqrt{\pi n_e}$.
Both intra-band and inter-band contributions to static screening are included in $g(q)$. For definiteness we will assume that the carrier density $n_e > 0 $.

The effective single-particle kinetic equation for the ${\bm k}$-diagonal part of the density matrix, $f_{\bm k}$, is derived from the quantum Liouville equation in the weak momentum scattering regime exactly as in Ref.~\onlinecite{Culcer_TI_ee_PRB11}
\begin{equation}\label{Kinetic}
    \frac{df_{\bm k}}{dt} + \frac{i}{\hbar}[H_{0{\bm k}},f_{\bm k}] + \hat{J}(f_{\bm k}) = - \frac{i}{\hbar}[H_{\bm k}^E,f_{\bm k}] + \frac{i}{\hbar}[\mathcal{B}^{MF}_{\bm k},f_{\bm k}],
\end{equation}
The scattering term $\hat{J}(f_{\bm k})$ in the first Born approximation is given by
\begin{widetext}
\begin{equation}\label{Scattering}
    \arraycolsep 0.3 ex\begin{array}{rl}\displaystyle
    \hat{J}(f_{\bm k}) = \frac{n_i}{{\hbar}^2}\lim_{\eta\to0}\int\frac{d^{2}k'}{(2\pi)^2}
    |\bar{U}_{{\bm k}{\bm k'}}|^{2}\int_{0}^{\infty}dt'e^{-\eta t'}  \{e^{-iH_{0{\bm k'}}t'/\hbar}(f_{\bm k}-f_{\bm k'})e^{iH_{0{\bm k}} t'/\hbar} + e^{-iH_{0{\bm k}}t'/\hbar}(f_{\bm k}-f_{\bm k'})e^{iH_{0{\bm k}'}t'/\hbar}\},
    \end{array}
\end{equation}
\end{widetext}
where $n_i$ is impurity density and $\bar{U}_{{\bm k}{\bm k}'}$ the potential of a single impurity. The mean-field electron-electron interaction term is
\begin{equation}\label{EEEffective}
    \mathcal{B}^{MF}_{\bm k}(f_{\bm k})=\frac{1}{(2\pi)^2}\int dk'k'\int_{0}^{2\pi}d\gamma \, V_{{\bm k}{\bm k'}} \, f_{{\bm k}'},
\end{equation}
where $\gamma = \theta' - \theta$ is the relative angle between wave vectors ${\bm k}$ and ${\bm k}'$, $V_{{\bm k}{\bm k'}}=V_{\bm q}$, and $\theta$ and $\theta'$ are the polar angles of ${\bm k}$ and ${\bm k}'$ respectively. The one-particle Hamiltonian $H_{{\bm k}{\bm k}'}^{ss'} = H_{0{\bm k}}^{ss'} \delta_{{\bm k}{\bm k}'} + H_{E{\bm k}{\bm k}'}\delta_{ss'} + U_{{\bm k}{\bm k}'}\delta_{ss'}$, where $H_{E{\bm k}{\bm k}'}$ is the electrostatic potential due to the driving electric field ${\bm E}$, and $U_{{\bm k}{\bm k}'} $ is the \textit{total} disorder potential.
The matrix element $\bar{U}_{{\bm k}{\bm k}'}$ of the RPA-screened Coulomb potential of a single impurity between plane waves is
\begin{equation}
  \bar{U}_{{\bm k}{\bm k'}}=\frac{Ze^2}{2\epsilon_0\epsilon_r[q+q_0g(q)]}
\end{equation}
where $Z=1$ is the ionic charge. Below we suppress the pseudospin indices $ss'$ and treat all quantities as $2 \times 2$ matrices.

We decompose $f_{\bm k}=n_{\bm k} \openone + S_{\bm k}$, with $n_{\bm k}$ a scalar part and $S_{\bm k}$ a pseudospin part, which can be expressed as $S_{\bm k}=\frac{1}{2}{\bm S}_{\bm k}\cdot{\bm \sigma}$, where the vector ${\bm S}_{\bm k}$ is real and its $z$ component is zero in equilibrium. Since the current operator is proportional to ${\bm \sigma}$, we are only interested in $S_{\bm k}$. We decompose $\hat{J}(f_{\bm k})=\hat{J}(n_{\bm k})+\hat{J}(S_{\bm k})$ and $\mathcal{B}^{MF}_{\bm k}(f_{\bm k})=\mathcal{B}^{MF}_{\bm k}(n_{\bm k})+\mathcal{B}^{MF}_{\bm k}(S_{\bm k})$, and $S_{\bm k}$ satisfies
\begin{widetext}
\begin{equation}\label{Sint}
    \arraycolsep 0.3 ex\begin{array}{rl}
    \displaystyle \frac{dS_{\bm k}}{dt}+\frac{i}{\hbar}[H_{0\bm k},S_{\bm k}]+\hat{J}(S_{\bm k}) =-\frac{i}{\hbar}[H_{\bm k}^E,S_{\bm k}]+\frac{i}{\hbar}[\mathcal{B}^{MF}_{\bm k}(S_{\bm k}),S_{\bm k}]
    \end{array}
\end{equation}
\end{widetext}
The interaction terms in Eq. (\ref{Sint}) can be
included iteratively, {\em i.e.} the solution is expanded in orders of $V$, i.e. $S_{\bm k}=\sum_{n}S_{E{\bm k}}^{ee,(n)}$,
$\mathcal{B}_{k}^{MF}=\sum_{n \geqslant 0 }\mathcal{B}_{k}^{MF,(n)}$ with $\mathcal{B}^{MF,(0)}_{\bm k}=0$, and
$\mathcal{B}^{MF,(n)}_{\bm k}=\frac{1}{(2\pi)^2}\int dk'k'\int_{0}^{2\pi}d\gamma V_{{\bm k}{\bm k'}}S_{E{\bm k}}^{ee,(n-1)}$.
Here $S_{E{\bm k}} \equiv S_{E{\bm k}}^{ee,(0)}$ in the absence of electron-electron interactions. Substituting the above expansion into the kinetic equation and keeping only terms linear in the electric field (note that $\mathcal{B}_{k}^{MF}$ is linear in ${\bm E}$), we obtain the equations below for each order $n\geqslant0$:
\begin{widetext}
\begin{equation}\label{Iteration}
    \arraycolsep 0.3 ex\begin{array}{rl}
    \displaystyle\frac{dS_{E{\bm k}}^{ee,(n)}}{dt}+\frac{i}{\hbar}\big[H_{0\bm k},S_{E{\bm k}}^{ee,(n)}\big]
    +\hat{J}\big[S_{E{\bm k}}^{ee,(n)}\big]
    \displaystyle=-\frac{i}{\hbar}\big[H_{\bm k}^{E},S_{E{\bm k}}^{ee,(n)}\big]+\frac{i}{\hbar}\big[\mathcal{B}^{MF,(n)}_{\bm k},S_{0{\bm k}} \big],
    \end{array}
\end{equation}
\end{widetext}
where  $S_{0{\bm k}}$ is the pseudospin-dependent part of the equilibrium density matrix, given below.

Following the method used in Ref.~\onlinecite{Culcer_TI_ee_PRB11}, we solve Eq.\ (\ref{Iteration}) for each $n$ by projecting onto directions parallel to (commuting with) and perpendicular to $H_{0{\bm k}}$, obtaining
\begin{equation}
\begin{array}{rl}
\displaystyle \frac{dS_{{\bm k}\parallel}}{dt}+P_{\parallel}\hat{J}(S_{\bm k}) = & \displaystyle D_{{\bm k}\parallel} \\ [1ex]
\displaystyle \frac{dS_{{\bm k}\perp}}{dt}+\frac{i}{\hbar}[H_{\bm k},S_{{\bm k}\perp}]+P_{\perp}\hat{J}(S_{\bm k}) = & \displaystyle D_{{\bm k}\perp},
\end{array}
\end{equation}
where the parallel and perpendicular components
\begin{equation}
\begin{array}{rl}
\displaystyle S_{{\bm k}\parallel} =  & \displaystyle (1/2)({\bm S}_{\bm k}\cdot\hat{\bm n}_{\bm k})({\bm \sigma}\cdot\hat{\bm n}_{\bm k})=
(1/2)s_{{\bm k}\parallel}\sigma_{{\bm k}\parallel} \\ [1ex]
\displaystyle S_{{\bm k}\perp} = & \displaystyle (1/2)({\bm S}_{\bm k}\cdot\hat{\bm m}_{\bm k})({\bm \sigma}\cdot\hat{\bm m}_{\bm k})=(1/2)s_{{\bm k}\perp}\sigma_{{\bm k}\perp}
\end{array}
\end{equation}
and the unit vector $\hat{\bm m}_{\bm k}=\hat{\bm z}\times\hat{\bm n}_{\bm k}$.

\section{Scattering term}
\label{sec:sct}

The scattering term does not mix the monopole ($n_{\bm k}$) and dipole ($S_{\bm k}$) components of the density matrix. Applying the decomposition ${\bm S}_{\bm k}=s_{{\bm k}\parallel}\hat{\bm n}_{\bm k}+s_{{\bm k}\perp}\hat{\bm m}_{\bm k}$ and ${\bm \sigma}=\sigma_{{\bm k}\parallel}\hat{\bm n}_{\bm k}+\sigma_{{\bm k}\perp}\hat{\bm m}_{\bm k}$, as well as $\hat{\bm n}_{\bm k'}=\cos(2\gamma)\hat{\bm n}_{\bm k}+\sin(2\gamma)\hat{\bm m}_{\bm k}$ and $\hat{\bm m}_{\bm k'}=-\sin(2\gamma)\hat{\bm n}_{\bm k}+\cos(2\gamma)\hat{\bm m}_{\bm k}$, to the expression for $\hat{J}(S_{\bm k})$, we obtain four projected terms as
\begin{equation}
\begin{array}{rl}
\displaystyle P_{\parallel}\hat{J}(S_{{\bm k}\parallel}) = & \displaystyle \frac{n_i \sigma_{{\bm k}\parallel}}{16\pi\hbar A}\int d{\theta}'|\bar{U}_{{\bm k}{\bm k'}}|^{2} (s_{{\bm k}\parallel}-s_{{\bm k'}\parallel}) (1 + \cos2\gamma) \\ [3ex]
\displaystyle P_{\perp}\hat{J}(S_{{\bm k}\parallel}) = &\displaystyle\frac{n_i \sigma_{{\bm k}\perp}}{16\pi\hbar A}\int d{\theta}'|\bar{U}_{{\bm k}{\bm k'}}|^{2} (s_{{\bm k}\parallel}-s_{{\bm k'}\parallel})\sin2\gamma
    \\ [3ex]
\displaystyle P_{\parallel}\hat{J}(S_{{\bm k}\perp}) = & \displaystyle \frac{n_i \sigma_{{\bm k}\parallel}}{16\pi\hbar A}\int d{\theta}'|\bar{U}_{{\bm k}{\bm k'}}|^{2} (s_{{\bm k}\perp}+s_{{\bm k'}\perp})\sin2\gamma
    \\ [3ex]
\displaystyle P_{\perp}\hat{J}(S_{{\bm k}\perp}) = & \displaystyle \frac{n_i \sigma_{{\bm k}\perp}}{16\pi\hbar A}\int d{\theta}'|\bar{U}_{{\bm k}{\bm k'}}|^{2}(s_{{\bm k}\perp}+s_{{\bm k'}\perp})(1 - \cos2\gamma)
\end{array}
\end{equation}

Using $q = 2k_F \sin\frac{\gamma}{2}$, we obtain a cumbersome expression for $|\bar{U}_{{\bm k}{\bm k'}}|$. We make the following Fourier expansions
\begin{equation}\label{Fourier}
\arraycolsep 0.3 ex
\begin{array}{rl}
\displaystyle |\bar{U}_{{\bm k}{\bm k'}}|^2(\gamma) = & \displaystyle \sum U_n e^{in\gamma} \\ [3ex]
\displaystyle (1 + \cos2\gamma) \, |\bar{U}_{{\bm k}{\bm k'}}|^2(\gamma) = & \displaystyle \sum W_n e^{in\gamma} \\ [3ex]
\displaystyle s_{{\bm k}\parallel} = & \displaystyle \sum s_{k\parallel n}e^{in\theta}.
\end{array}
\end{equation}
The parallel projection of the scattering term
\begin{equation}
    P_{\parallel}\hat{J}(S_{{\bm k}\parallel}) = \frac{n_i}{8\hbar A}\sum_n (W_0-W_n)s_{k\parallel n}e^{in\theta}\sigma_{{\bm k}\parallel},
\end{equation}
where $W_{-n}=W_{n}$ since $|\bar{U}_{{\bm k}{\bm k'}}|^2(\gamma)$ and $1 + \cos2\gamma$ are even functions of $\gamma$.

\section{Transport in non-interacting BLG}
\label{sec:nonint}

We briefly review transport in the absence of interactions.  Writing $S_{\bm k} = S_{0{\bm k}} + S_{E{\bm k}}$
and keeping terms to o linear order in ${\bm E}$ we obtain
\begin{equation}
    \frac{dS_{E{\bm k}}}{dt}+\frac{i}{\hbar}[H_{0\bm k},S_{E{\bm k}}]+\hat{J}(S_{E{\bm k}})=D_{E{\bm k}}
\end{equation}
where the electric-field driving term
\begin{equation}
\arraycolsep 0.3 ex
\begin{array}{rl}
\displaystyle D_{E{\bm k}} = & \displaystyle \frac{e{\bm E}}{\hbar}\cdot\pd{S_{0{\bm k}}}{\bm k}
    = \frac{1}{2} \, d_{E{\bm k}\parallel} \sigma_{{\bm k}\parallel} + \frac{1}{2} \,  d_{E{\bm k}\perp} \sigma_{{\bm k}\perp} \\ [3ex]
\displaystyle d_{E{\bm k}\parallel} = & \displaystyle \frac{e{\bm E}\cdot{\hat{\bm k}}}{\hbar}
    \bigg(\frac{\partial f_{0+}}{\partial k}-\frac{\partial f_{0-}}{\partial k}\bigg) \\ [3ex]
\displaystyle d_{E{\bm k}\perp} = & \displaystyle \frac{e{\bm E}\cdot\hat{\bm \theta}}{\hbar k}(f_{0+}-f_{0-}),
\end{array}
\end{equation}
in which $f_{0\pm} \equiv f_0 (\varepsilon_{{\bm k}\pm})$, with $f_0$ the Fermi-Dirac distribution function, and $S_{0{\bm k}}=(1/2)(f_{0+}-f_{0-})\sigma_{{\bm k}\parallel}$. We assume the temperature to be absolute zero, thus
\begin{equation}
\arraycolsep 0.3ex
\begin{array}{rl}
\displaystyle d_{E{\bm k}\parallel} = & \displaystyle -\frac{e{\bm E}\cdot{\hat{\bm k}}}{\hbar}\delta(k-k_F) \\ [1ex]
\displaystyle S_{{\bm k}\parallel} = & \displaystyle -\frac{\tau e{\bm E}\cdot\hat{\bm k}}{4\hbar}\delta(k-k_F)\sigma_{{\bm k}\parallel},
\end{array}
\end{equation}
where the momentum relaxation time
\begin{equation}
    \tau = \frac{8\hbar A}{n_i(W_0-W_1)}.
\end{equation}
The velocity operator is given by
\begin{equation}
{\bm v}_{\bm k} = \frac{1}{\hbar} \, \pd{H_{0{\bm k}}}{\bm k}.
\end{equation}
The expectation value of the current density operator is $\bkt{{\bm j}} = \displaystyle -eg_vg_s\int\frac{d^2k}{(2\pi)^2}\mathrm{Tr}[{\bm v}_{\bm k}S_{\bm k}]$, where Tr acts in pseudospin space, and $g_v=g_s=2$ are the valley and spin degeneracies, respectively. Substituting $S_{\bm k}=(1/2)(s_{{\bm k}\parallel}\sigma_{{\bm k}\parallel}+s_{{\bm k}\perp}\sigma_{{\bm k}\perp})$, taking ${\bm E}\,\parallel\,{\bm x}$, the velocity operator is $v_x=v_{x{\bm k}\parallel}\sigma_{{\bm k}\parallel}+v_{x{\bm k}\perp}\sigma_{{\bm k}\perp}$, where $v_{x{\bm k}\parallel}=2Ak\cos\theta/\hbar$ and $v_{x{\bm k}\perp}=-2Ak\sin\theta/\hbar$, and assuming that $\varepsilon_F \tau/\hbar \gg 1$,  it follows that the conductivity is
\begin{equation}
    \sigma_{xx}^{\mathrm{bare}} = \frac{Ae^2k_F^2\tau}{\pi\hbar^2}.
\end{equation}
The Zitterbewegung (interband coherence)  contribution to the conductivity,
plays an essential role for the minimum conductivity which survives at the charge neutrality point,\cite{Culcer_BLG_transp_PRB09, Culcer_MLG_transp_PRB08, Trushin_BLG_MinCond_PRB10, David_BLG_BS_MinCond_PRB12},
as in the MLG \cite{Culcer_MLG_transp_PRB08, Katsnelson_EPJB06} and topological insulators (TI) cases, \cite{Culcer_TI_transp_PRB10, Culcer_TI_PhysE12} but is next-to-leading order in the
small parameter $\hbar/\varepsilon_F \tau$ and not considered here.

\section{Interaction renormalization}
\label{sec:int}

Interactions in equilibrium BLG renormalize the constant $A$ (that is, they renormalize the Fermi velocity).\cite{BorghiPolini_MLGBLG_Fermi_enhancement_SSC09} This does not make any qualitative changes to our arguments and derivation below, and for simplicity we assume henceforth that $A$ represents the renormalized $A$. In this section we will determine the mean-field interaction correction $\mathcal{B}_{\bm k}^{MF,(1)}$. From Eq.\ (\ref{Iteration}) it is evident that only the part of $\mathcal{B}_{\bm k}^{MF,(1)} \propto \sigma_{{\bm k}\perp}$ contributes to the dynamics. We abbreviate $l=k/k_F$ and
\begin{equation}\label{firstB}
    \mathcal{B}_{\bm k}^{MF,(1)}=-\frac{\tau e^3E_x}{16\pi\epsilon_0\epsilon_r\hbar}\, I_{ee}^{(1)}(l,n_e)\sin\theta\sigma_{{\bm k}\perp},
\end{equation}
where the dimensionless quantities
\begin{widetext}
\begin{equation}\label{Iee}
\arraycolsep 0.3 ex
\begin{array}{rl}
\displaystyle I_{ee}^{(1)}(l,n_e) = &\displaystyle -\int_{0}^{2\pi}\frac{d\gamma}{2\pi}\, \frac{\sqrt{\pi n_e}\sin\gamma\sin(2\gamma)}
    {\sqrt{\pi n_e(l^2+l'^2-2ll'\cos\gamma)}+q_0g(l,l',\gamma)} \\ [3ex]
\displaystyle g(l,l',\gamma) = &\displaystyle \frac{1}{2}\sqrt{4+(l^2+l'^2-2ll'\cos\gamma)^2}
    -\ln\bigg[\frac{1}{2}+\frac{1}{4}\sqrt{4+(l^2+l'^2-2ll'\cos\gamma)^2}\bigg].
    \end{array}
\end{equation}
\end{widetext}
The driving term arising from $\mathcal{B}_{\bm k}^{MF,(1)}$ contributes only to $S_{{\bm k}\perp}$, and we easily find
that
\begin{equation}
    S_{E{\bm k}\perp}^{ee,(1)}=\frac{\tau eE_xq_0}{16\hbar k^2}I_{ee}^{(1)}(l,n_e)f_{0}
    \sin\theta\sigma_{{\bm k}\perp}.
\end{equation}
An additional correction arises from the equation
\begin{equation}
    P_{\parallel}\hat{J}[S_{E{\bm k}\parallel}^{ee,(1)}]=-P_{\parallel}\hat{J}[S_{E{\bm k}\perp}^{ee,(1)}],
\end{equation}
Taking this into account, the first-order correction to the diagonal conductivity is
\begin{equation}
    \sigma_{xx}^{(1)}=\frac{q_0[1+\beta(n_e)]}{4\sqrt{\pi n_e}}I_{ee}^{(1)}(n_e)\sigma_{xx}^{\mathrm{bare}}
\end{equation}
with $\beta(n_e)=(U_1-U_3)/(2U_0+2U_2-3U_1-U_3)$, in which $U_n$ is the $n$-th Fourier coefficient of $|U_{{\bm k}{\bm k'}}|^2$ as defined in Eq.\ (\ref{Fourier}), and $I^{(1)}_{ee}(n_e)=\int_{0}^{1}dl I^{(1)}_{ee}(l,n_e)$. Notice that
$\beta$ vanishes for momentum-independent (short-range) interactions.

The angular structure of $I_{ee}^{(1)}(l,n_e)$ in Eq.\ (\ref{Iee}) can be understood by noting that the electric field driving term is responsible for the factor of $\sin\gamma$, while the factor of $\sin2\gamma$ arises from the projection of the pseudospin component parallel to $\hat{\bm k}$ onto the pseudospin component parallel to $\hat{\bm k}'$. For the massless Dirac cones of TI and MLG, where the (pseudo)spin winds around the Fermi surface only once, these terms (i.e. the electric-field driving term and the pseudospin projection) have the same rotational symmetry and reinforce each other. In BLG, the fact that the pseudospin winds twice around the Fermi surface is crucial, and makes the angular structure of this term entirely different from MLG and TI. As $n_e \rightarrow 0$, $I_{ee}^{(1)}(l,n_e)$ averages to zero over the Fermi surface. Its effect at small $n_e$ is therefore correspondingly small. In this context, it must also be noted that $q_0$ is set by $t_\perp$, the (sizable) interlayer hopping parameter, and that $q_0 \gg k_F$ even at $n = 10^{13}$cm$^{-2}$, which in transport ordinarily constitutes a large carrier density ($k_F \approx 5.5 \times 10^{8}$m$^{-1}$).

We retain only terms of linear order in the external electric field. Under these conditions, the following two equations are sufficient to obtain all higher order terms $(n>1)$,
\begin{equation}
    \arraycolsep 0.3 ex\begin{array}{rl}
    \displaystyle\frac{dS_{E{\bm k}\perp}^{ee,(n)}}{dt}+\frac{i}{\hbar}[H_{\bm k},S_{E{\bm k}\perp}^{ee,(n)}]
    =&\displaystyle\frac{i}{\hbar}[\mathcal{B}_{\bm k}^{MF,(n)},S_{0{\bm k}}]\\[3ex]
    \displaystyle P_{\parallel}\hat{J}[S_{E{\bm k}\parallel}^{ee,(n)}]=&\displaystyle -P_{\parallel}\hat{J}[S_{E{\bm k}\perp}^{ee,(n)}].
    \end{array}
\end{equation}
In the higher orders ($n>1$), $S_{E{\bm k}}^{ee,(n-1)}$ is fed into $\mathcal{B}^{MF,(n)}_{\bm k}$, which then determines $S_{E{\bm k}}^{ee,(n)}$, completing the self-consistent loop. Repeating the iteration, we obtain a general formula for $I_{ee}^{(n)}(n_e)$ for $n>1$, i.e.
\begin{widetext}
\begin{equation}
    \arraycolsep 0.3 ex\begin{array}{rl}
    \displaystyle I_{ee}^{(n)}(n_e)=&\displaystyle (-\sqrt{\pi n_e})^n\bigg[\prod_{i=1}^{n-1}\int_{0}^{1}
    \frac{dl_i}{l_i}\int_{0}^{2\pi}\frac{d\gamma_i}{2\pi}\bigg]\int_{0}^{1}dl_n\int_{0}^{2\pi}\frac{d\gamma_n}{2\pi}\\[3ex]
    &\displaystyle\bigg[\prod_{i=1}^{n-1}\frac{[\cos\gamma_i\cos(2\gamma_i)+\beta(n_e) \sin\gamma_i\sin(2\gamma_i)]}{\sqrt{\pi n_e(l_i^2+l_{i+1}^2-2l_il_{i+1}\cos\gamma_i)}+q_0g(l_i,l_{i+1},\gamma_i)}\bigg]\\[3ex]
    &\displaystyle\frac{\sin\gamma_n\sin(2\gamma_n)}{\sqrt{\pi n_e(l_n^2+1-2l_n\cos\gamma_n)}+q_0g(l_n,1,\gamma_n)},
    \end{array}
\end{equation}
\end{widetext}
and the $n$th-order interaction correction to the conductivity is $\sigma_{xx}^{(n)}=[1+\beta(n_e)](q_0/\sqrt{16\pi n_e})^nI_{ee}^{(n)}(n_e)\sigma_{xx}^{\mathrm{bare}}$. Finally, the exact conductivity is
\begin{widetext}
\begin{equation}
    \sigma_{xx} = \sigma_{xx}^{\mathrm{bare}} \, \left\{1+[1+\beta(n_e)] \sum_{n>0}\left(\frac{q_0}{\sqrt{16\pi n_e}}\right)^nI^{(n)}_{ee}(n_e)\right\}.
\end{equation}
\end{widetext}
We refer to $\sigma_{xx}$ as the full conductivity, to distinguish it from the bare conductivity $\sigma_{xx}^{\mathrm{bare}}$. The appearance of $\beta(n_e) \ll 1$ is related to the factor of $2\gamma$ appearing in the mean-field interaction term.

\section{Discussion}
\label{sec:disc}

In equilibrium electron-electron interactions renormalize the band parameter $A$.\cite{BorghiPolini_MLGBLG_Fermi_enhancement_SSC09}
Here we have obtained an exact result, within a self-consistent Hartree-Fock approximation, for the
influence of interactions on the conductivity of doped metallic BLG.
Below we comment on the sign of the interaction renormalization, its size, and its density dependence.

\begin{figure}[tbp]
\bigskip
\includegraphics[width=\columnwidth]{sigmavsn.pdf}
\caption{\label{sigmavsn} Fractional change in the conductivity $\sigma_{xx}/\sigma_{xx}^{bare}$ (black), and the parameter $\beta$ (blue), as a function of the carrier density $n_e$.}
\end{figure}

We recall that a charge current in BLG
necessarily gives rise to a steady-state pseudospin polarization.
Consequently, $\sigma_{xx}$ may be understood by considering pseudospin dynamics on the Fermi surface.
The renormalization reflects the interplay of pseudospin-momentum locking embodied in $H_{0{\bm k}}$ and the mean pseudospin-field $\mathcal{B}^{MF}_{\bm k}$ arising from electron-electron interactions.
The pseudospin of one carrier on the Fermi surface at ${\bm k}$ is subject to two competing interactions. The effective field $Ak^2\hat{\bm n}_{\bm k}$ tends to align the spin with its band value.
The mean-field $\mathcal{B}^{MF}_{\bm k}$ tends to align a pseudospin at ${\bm k}$ against the total existing pseudospin polarization. The net result is a small steady-state rotation of the pseudospin at each ${\bm k}$ away from the direction of the effective field $Ak^2\hat{\bm n}_{\bm k}$. Thus the overall effect of interactions is to align individual pseudospins in the direction opposite to that of the existing pseudospin polarization.

Since the renormalization is negative, interactions cannot cause $\sigma_{xx}$ to diverge, and
there is no possibility of a Fermi-surface instability.
The conductivity is therefore reduced by interactions, which is reminiscent of the result of Ref.~\onlinecite{Barlas_graphene_chirality_correlation_PRL07}.
One may gain insight by further analyzing the functional form of the ratio $\sigma_{xx}/\sigma_{xx}^{bare}$, concentrating on its density dependence. Taking $A=0.71\,\mathrm{eV\cdot nm^2}$, as well as $\epsilon_r=1$ for simplicity, the wave vector $q_0=e^2/(2\pi\epsilon_0\epsilon_rA)=4.0\,\mathrm{nm^{-1}}$. As discussed before, in all realistic transport regimes $k_F=\sqrt{\pi n_e}\ll q_0$. In this low-doping regime, $\beta(n_e)$ becomes independent of $n_e$ for all $U_n\propto n_e^{1/2}$, and the conductivity simplifies to
\begin{widetext}
\begin{equation}
    \arraycolsep 0.3 ex\begin{array}{rl}
    \displaystyle{\frac{\sigma}{\sigma^{\mathrm{bare}}}}
    =&\displaystyle 1+(1+\beta)\sum^{\infty}_{n=1}
    \left(-\frac{1}{4}\right)^n\left[
    \prod_{i=1}^{n-1}\int_{0}^{1}\frac{dl_i}{l_i}\int_{0}^{2\pi}\frac{d\gamma_i}{2\pi}\right]
    \int_{0}^{1}dl_n\int_{0}^{2\pi}\frac{d\gamma_n}{2\pi}\\[3ex]
    &\displaystyle\left[\prod_{i=1}^{n-1}\frac{\cos\gamma_i\cos(2\gamma_i)
    +\beta\sin\gamma_i\sin(2\gamma_i)}{g(l_i,l_{i+1},\gamma_i)}\right]
    \frac{\sin\gamma_n\sin(2\gamma_n)}{g(l_n,1,\gamma_n)}.
    \end{array}
\end{equation}
\end{widetext}
In this limit the full conductivity has almost exactly the same density dependence as the bare conductivity. The behavior at densities commonly encountered in transport is illustrated in Fig.~\ref{sigmavsn}. The small size of the renormalization makes its detection challenging. At small $n_e$, the ratio tends to zero as a result of the vanishing of angular integral appearing in $I_{ee}^{(1)}(l,n_e)$ in Eq.\ (\ref{Iee}). Steady-state expectation values are determined by the electric-field driving term, which contains a factor of ${\bm E}\cdot\hat{\bm k}$. Unlike MLG/TI, the pseudospin is not a linear function of $\parallel \hat{\bm k}$ (or $\hat{\bm \theta}$), but is characterized by a winding number of $2$. As a result of this, in BLG the interaction renormalization of the conductivity/pseudospin polarization is negligible when $k_F \ll q_0$. At large $n_e$, the behavior of $\sigma_{xx}$ is summarized by
\begin{widetext}
\begin{equation}\label{highdoping}
    \arraycolsep 0.3 ex\begin{array}{rl}
    \displaystyle\frac{\sigma}{\sigma^{\mathrm{bare}}}
    =&\displaystyle 1-\frac{(1+\beta)q_0}{\sqrt{16\pi n_e}}
    \int_{0}^{1}dl\int_{0}^{2\pi}\frac{d\gamma}{2\pi}\frac{\sin\gamma\sin(2\gamma)}{\sqrt{l^2+1-2l\cos\gamma}}.
    \end{array}
\end{equation}
\end{widetext}
In this regime the ratio $\sigma_{xx}/\sigma_{xx}^{bare} \propto 1/\sqrt{n_e}$, decreases with increasing carrier density, but for this trend to be noticeable one requires $\sqrt{\pi n_e} \gg q_0$, which can never be reached in practice.

It is enlightening to compare the interaction renormalization of the conductivity in BLG with the case of TI and MLG. In TI, as in MLG, the interaction renormalization of the conductivity is density independent and again accounts for only a fraction of the total conductivity. At first sight, it seems striking that the same observation holds in BLG. Retracing the mathematical steps, the first order correction to the density matrix in TI is \cite{Culcer_TI_ee_PRB11}
\begin{equation}
    S_{E{\bm k}\perp}^{ee,(1)}=\frac{eE_xr_s\tau I_{ee}^{(1)}(l,r_s)}{16\hbar k}f_{0}\sin\theta\sigma_{{\bm k}\perp},
\end{equation}
hence $1/k$ in TI corresponds to $k_F/k^2$ in BLG, which results in approximately the same density dependence. The reason for this correspondence is that the TI Hamiltonian is $\propto k$ while the BLG Hamiltonian is $\propto k^2$, so the steady-state (pseudo)spin densities differ by a factor of $k$. At the same time, screening also differs by a factor of $k$ between the two, and the additional density dependences arising from these two factors effectively cancel out. Although the density dependence is different from TI, the correction is more complex but still weak. At very low-energies trigonal warping terms must be added to the BLG band structure,
leading to the formation of Dirac cones. In this limit, we would expect that the
interaction correction to conductivity we discuss, would cross over to a form similar
to that appropriate for MLG, TI's and other Dirac cone systems provided that
this regime is not preempted by interaction-driven phase transitions to gapped states. \cite{Zhang_BLG_SpontSymBrk_PRB10, Zhang_BLG_Ordered_PRB12}

\section{Summary}
\label{sec:sum}

We have calculated the effect of non-equilibrium interaction self-energy effects on the conductivity of metallic bilayer graphene.  Although these effects can be large in some systems, in BLG they give rise to a negative renormalization of the conductivity which is small and has a weak density dependence. This property follows from
the large interlayer tunneling parameter in BLG, which leads to a $\pi$-band pseudo spin
with a momentum-space winding number of $2$ that is incommensurate with the
velocity winding number of $1$.   The corresponding effects could be larger
when a gap is opened using a bias voltage or when a magnetic field is present.

This work is supported by the National Natural Science Foundation of China under grant number 91021019.
AHM was supported by DOE grant DE-FG03-02ER45958 and by Welch Fiundation grant No. TBF1473.
We gratefully acknowledge discussions with S.~Das Sarma.

redpajama_set_name: RedPajamaArXiv


text:
SENATOR DANIEL AKAKA, GOVERNOR GEORGE ARIYOSHI, GOVERNOR BENJAMIN CAYETANO: OHA's Power Grab will harm State's ability to continue trust responsibility to Native Hawaiians
July 27, 2016 — The following is an excerpt from a letter to President Barack Obama published in the Hawai'i Free Press:
We oppose the proposed expansion of the Papahanaumokuakea Marine National Monument (PMNM).Native Hawaiian rights and Hawaii State rights have not been considered and there is no transparency in this process. No economic impact study was taken to determine the impact of this proposed expansion.Hawai'i is the only State in the union comprised of small islands surrounded by the ocean and remotely located thousands of miles from any other land mass. We depend on the ocean for food, livelihood,recreation, and the perpetuity of traditional native Hawaiian cultural practices.
Hawaii is the only State that met the Convention on Biological Diversity's Aichi Target 11 to protect 10 percent of coastal and marine areas by 2020. Nearly 23 percent of the waters surrounding Hawai'i are in no-take reserves even though scientists recommend protecting 20 percent of the waters to maintain healthy oceans.
Your office is considering using the Antiquities Act of 1906 to extend the protection of the waters and submerged lands from 50 to 200 miles offshore of the Northwest Hawaiian Islands – we oppose that.That is a 350 percent expansion of the PMNM from 140,000 square miles to 583,000 square miles. The proposed monument area is equal in size to the landmass of all of the West Coast States (Washington,Oregon and California) and Texas combined.
The proposed expansion would include the entire U.S. exclusive economic zone (EEZ) surrounding the Northwestern Hawaiian Islands (i.e., 53 percent of the EEZ around the State of Hawai'i). The expansion would prohibit the State of Hawai'i from using the living and non-living resources within the U.S. EEZ as provided for in the United Nation's Convention on the Law of the Sea, Proclamation 5030 on the Exclusive Economic Zone of the United States, and the Magnuson-Stevens Fishery Conservation and Management Act (MSA).
See the full letter at the Hawai'i Free Press
Categories: Washington Tags: Antiquities Act, Benjamin Cayetano, Convention on Biological Diversity's Aichi Target 11, Daniel Akaka, George Ariyoshi, Hawaii, Northwestern Hawaiian Islands, Pacific, Papahanaumokuakea Marine National Monument


Once upon a time, a hungry fox was roaming around here and there searching for food. Because of hunger, she was feeling weak and tired. Fortunately, she came to a garden where she saw a bunches of grapes laden which were looked quite ripe and juicy.
The fox looked at the grapes with longing eyes and licked his chops. But the bunches were too high for her and she was feeling weak. She sat down for a while to take some rest. After some time Then she jumped as high as he could, to get at the grapes. But she failed to reach them.
Then she again rested for some time and made another bold attempt, but was unlucky for the second time also.
Forced to give up trying anymore and she walked away and instead of accepting his failure, she remarked "the grapes appeared to be ripe and juicy, but now I see them to be quite sour."
This story tells us that, people generally hate what they can't get.