text:
Why is People's Court unavailable on streaming services and other media?
People's Court became my guilty pleasure a few years ago and I've been happily watching new episodes daily at lunch since. However, there are not nearly enough produced each year to keep up with my viewing schedule and I often find myself running out. Thus lead me to the obvious step of trying to find and purchase old seasons.
I searched five different paid streaming services without success. Dish Network does not have it on-demand. Neither Amazon nor other online retailers carry the show on-demand nor on DVD. Searching Google didn't help much on finding old episodes anywhere. It's nowhere to be found through less official channels either.
I've never seen anything like this before; every other movie or show, even those from the 80s, 70s, 60s, or 50s, seems available somewhere.
What causes People's Court to be so universally unavailable?
Is this a purposeful decision by the studio, or a result of it not being deemed profitable enough?
production reality-tv availability peoples-court
Vishwa
NicholasNicholas
Welcome to Movies and TV SE!. Although this is an interesting question, some areas in your question may render this off topic. I've edited it to make less off-topic material. but feel free to do more edits or rollback to your original post. – Vishwa Jul 30 '19 at 3:30
"Guilty" pleasure. I see what you did there. ;-) – BrettFromLA Jul 30 '19 at 17:41
Mostly because of deals with networks.
Consider this - I have the same feeling about Jeopardy. You can't even find a compilation from way back on VHS. Nothing official. Netflix and contour, etc, they only offer what is packaged for whatever reasons they decide, not necessarily public appeal.
The thought behind this is that people will have a higher probability of tuning into the new slots, with paid advertising, if they arent given the option to binge in other media where the advertising rituals aren't as formatted as they were back in the good ol days (you know, when cable was free of ads). I don't have any sources to reference this and I am not sure where to find them. That's massively devalues my answer, but I thought I would chime in and let you and others know this is what I was told in my own searches for an archive of Jeopardy. No idea why things like Bewitched, Game of Thrones, etc, are not bound by these same rules unless they have higher probabilities of profits over expenses. It could be there just isn't a proven market for things that fall into the category of reality television relevant to a specific era... then again, I can get an archive of Ghost Hunters at target, so I cannot be wholly sure.
You may be able to find people who have recorded them on unofficial channels and peer to peer networks, but naturally that is inherently illegal so officially I advise not to look into that.
Good luck though. Maybe the K-Mart at 400 Oak street has it. Next to the underwear.
Kai QingKai Qing
Next to the underwear... that's somewhat specific ;) – Vishwa Jul 30 '19 at 3:28
@Vishwa - lol yeah, It's a rainman joke. He was obsessed with people's court and only bought underwear from the K-Mart at 400 Oak Street. – Kai Qing Jul 30 '19 at 4:02
Regarding why the same doesn't apply to GoT or Bewitched, etc... Consider that reality TV and game shows that have been running for literally decades will have a lot of episodes. Making a deal for the whole shebang will be very expensive, even if the network is willing to do it. Standard TV dramas have a limited number of seasons (generally less than 10 in most cases,) so buying the whole thing is more feasible. – Steve-O Jul 31 '19 at 13:14
@Steve-O for sure. I wasn't really questioning it as a complete package because technology of yesterday would have been exactly what you say. Too expensive. But some shows had like compilation packages in the DVD era, and now with streaming there's pretty much no excuse not to unless the quality of their archives would generate more complaints than subscriptions. It would be neat to have a set with commercials and things from that era. I just watched some commercials from the early 80's just to see if they were what I remembered. There's a market out there for the odd things. – Kai Qing Jul 31 '19 at 15:36
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Open the jam-access cover on top of the ADF, see picture below.
Open the roller-access cover, see picture below.
Lower the ADF pickup roller assembly, see picture below.
Slide the roller assembly toward the front of the printer to remove it.
Install the new roller; notice that the roller assembly is "keyed" so make sure as you install the new assembly that you position the hex-shaped fitting on the shaft towards the rear of the printer.
Open the jam-access cover, see picture below.
Lift the ADF input tray upwards, see picture below.
Push in on the latch shown in picture below (blue arrow), to release the separation pad assembly.
Next, lower the ADF input tray , and then lift the separation pad assembly up.
Remove the separation pad , see picture below.
Often the spring underneath the separation pad comes loose; re-install the separation pad spring as shown in picture below.
Install the new separation pad, and close the cover.
Now, we will reset the Counter for this ADF parts kit. From the printer's control panel --> Open the Administration menu, choose Manage Supplies, choose Reset Supplies, select New Document Feeder Kit, and choose Reset.


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text:
exports.checkBaseModules = function () {
	var value = true;
	value &= checkModule('fs');
	value &= checkModule('console');
	value &= checkModule('binary');
	value &= checkModule('shell');
	value &= checkModule('system');
	return value;
}

exports.checkRequireWorks = function() {
	var module = require('fs');
	if(typeof module.file === 'undefined') {
		return false;
	}

	return true;
}

exports.checkBaseModules.description = "checking wether base modules are present";
exports.checkRequireWorks.description = "checking wether require works";

redpajama_set_name: RedPajamaGithub


text:
Preliminary Stage
From the project inception in November 2010, the necessary preliminary stages have been progressed to the extent that, at May 2011, the situation was as follows:-
A project management team has been formed
A Project Brief has been finalised.
Local Fund Raising has allowed the Project to proceed during this phase.
A Design Team has been selected via a tender competition, and is appointed.
Consultation with local the local school has progressed so as to discuss their input and the ways in which they may participate in the Project, and gain from use of the completed facility.
Local information is being gathered to form part of the information for any display material.
Preliminary drawings and specifications are prepared.
A Project Cost Plan is in place.
Initial fund raising has begun.
Communications within the Team has been established via an e-mail site, and a web site has been established.
Progress from May 2011 to April 2012
Since this time, good progress has been made in a variety of areas.
Funding for the Project has been secured, so that it is now possible to move forward to the selection and appointment of a contractor. An advertisement requesting notice of interest from potentail tenderers, has been published in the Press.
Tender drawings and documents are in the process of being prepared.
The preparation of a "memory bank" has been progressed, and liaison has continued with local schools to develop teaching opportunities associated with the Project.
After preliminary input from the project team, class teacher, Helen Black, developed a resource pack comprised of teaching plans and related worksheets containing suggestions for a wide range of educational experiences which support a Curriculum for Excellence. The pack was piloted with her Primary seven class in the autumn term (2011).
The culmination of the term's work and the highlight of the topic was the making of a short film 'A Well in Time' written, acted and shot on location in Scotlandwell by Mrs Black and her class. The children took on roles of characters who have featured in the history of the Wash House. The edited version was screened to a highly appreciative audience of parents and a representative of the project team.
Such was the success of this topic that Perth and Kinross Council deemed it to be an example of good practice which should be shared nationally. Consequently, Mrs Black and her Head Teacher colleague, Louise Gordon, were invited to present the project to senior educational officers, as well as representatives of environmental and heritage groups, at the Scottish Outdoor Learning Conference in Stirling in March.
During the summer term (2012) some further pieces of historical evidence will be added to the resource pack and an information leaflet for other local schools will be developed. To coincide with the opening of the restored building, the finalised resource pack will be made available to all schools by being uploaded to GLOW, the Scottish Schools' Intranet.
Architects North Elevation Drawing
With the help of local councillor Willie Robertson, the descendants of the owners of Well Road have been traced. This represents a considerable step forward in terms of an eventual resolution of the problems with the state of the road, which continues to deteriorate. The descendants, whi now live in Canada, are now to be contacted by Scotlandwell in Bloom and the residents of Well Road to determine whether their is the possibility of a transfer of titile that could then lead to unlocking funding for its repair.
Overall Project Programme/Progress
As of the beginning of May 2012, tender information for the construction works is well advanced, with Bills of Quantities and Preliminaries documents being prepared.
Building Warrant Application is to be made on the 18th May, with a decision expected by 1st. June.
Revised target dates, for the tender period and construction works, are now :-
Issue of Tenders – w/e. 1st. June 2012, for return by the 22nd., and an appointment by w/e. 6th. July
Beginning of Construction Work – 23rd. July 2012
Project Completion (Construction Work) – w/e. 23rd. November 2012
Progress On Site
Beveridge Builders of Perth were appointed as Main Contractor in July after a close fought tender competition.
A start up meeting was held at the end of July, and work was planned to start on site on the 30th July, for completion in October.
Construction progress was monitored, and you can see how the project progressed by looking on the page entitled Construction Progress
The construction progress also shows the completed project
Scotlandwell wash house
Progress (March 2013)
Scotlandwell
Costs/Funders

redpajama_set_name: RedPajamaCommonCrawl


text:
Schaenicoscelis is een geslacht van spinnen uit de familie lynxspinnen.

Soorten

 Schaenicoscelis concolor Simon, 1898
 Schaenicoscelis elegans Simon, 1898
 Schaenicoscelis exilis Mello-Leitão, 1930
 Schaenicoscelis guianensis Caporiacco, 1947
 Schaenicoscelis leucochlora Mello-Leitão, 1929
 Schaenicoscelis luteola Mello-Leitão, 1929
 Schaenicoscelis viridis Mello-Leitão, 1927

Lynxspinnen

redpajama_set_name: RedPajamaWikipedia


Gloomhaven is finally arriving at the end of next week, for those of you with preorders we will post them as soon as possible (on Thursday or Friday). For those of you hoping to get a copy, we do have a few extras, but we also have a waiting list to go through so it's not likely we'll have any for general sale yet. The publisher has said that there is print-run going on now with possibly a small restock in around a month, but a large one (20,000) expected to arrive around May. So there will be plenty, but you may have to be patient.
We've not had a newsletter in a few weeks, so below there's not just next week's new arrivals, but also some from the last couple of weeks as well.
We are excited to try this expansion to the popular dice-placement game ourselves!


Plumbing Replacements is a type of skill with various aspects and many ways to use copper pipe to create all kinds of beautiful and useful pieces. If you are considering Plumbing as a Handyman St Albans, the information in this article can help you. The information you glean here can be all you need to get a new project underway.
When doing any Plumbing Replacements, safety is a big concern. Always purchase the necessary safety equipment to avoid injury. Never remove any guards off of your power tools that are there to protect you. These simple things can help protect you from accidents.Try using duct tape to create a level spot. If you've used your table saw on a base that's mobile, you should be able to easily pull it in and out. To really finish it up, find a level spot on your floor. This also helps you saw boards without obstruction. Mark your wheel positions using duct tape that is brightly colored, and then roll the saw to that same flat spot each time you need to saw.
Always follow the owner's manual when using one of your Plumbing tools. Not knowing the manual's recommendations can result in injury or failure of your tool, and you surely do not want either of these to happen to you. If you have not yet read your manuals do so right away!Always clean up sanding dust thoroughly before staining or applying a topcoat. If you want a smooth finish, dust is your enemy. Use a vacuum over blowing dust into the air because it settles back onto the copper pipe, and use a damp cloth to ensure all dust is removed from the copper pipe in your final clean-up prior to staining or applying a top coat.
Before even beginning a Plumbing Replacements, make sure you have an adequate and proper place to work in. You definitely don't want your living space filled with sawdust. Some Plumbing supplies, such as stains, varnish and paint strippers, have noxious fumes. Ideally, you will have a detached garage or a shed to work in since an outside space is an ideal location.Organize your Plumbing space. There are few things more irritating than looking for a tool when you need it, and not making any headway in the process. Missing and misplaced tools can lead to major project delays. Keeping organized is a big help. In fact, pulling out the tools that you'll need before a project is a smart thing to do.
Use some affordable filters for collecting fine dust. The filters and micro-filtering bags made to catch this dust can get pricy after several replacements. Try using the ones that are sold for use in household vacuums.
You can buy the cheap ones and easily modify them to fit your shop vacuum. Cut off the top a bit past the small opening. Turn the whole thing inside out so that airflow still flows in the usual direction. Slip it over your foam filter using the retaining ring to keep it in place.
Clearly, Plumbing is a practical and enjoyable Handyman St Albans. The advice provided here can assist you in learning more about this incredible skill so that you can create incredible works of art.


These knitted cuffs are a pair of open tube wrist warmers that cover the forearm, wrists and bottom of the hands up to the fingers. The cuffs are knit in the round using a shell stitch pattern.
CO 50 sts using preferred method.
Join to knit in the round being careful not to twist, pm to mark beginning of the rnd.
Round 2: *p1, k1, p1, k1, (yf, k1, rep 6 times). Repeat from * to end of rnd.
Round 3: *p1, k1, p1, sl1, k1, psso, k9, k2tog. Repeat from * to end of rnd.
Round 4: *p1, k1, p1, sl1, k1, psso, k7, k2tog. Repeat from * to end of rnd.
Round 5: *p1, k1, p1, sl1, k1, psso, k5, k2tog. Repeat from * to end of rnd.
When the colour sequence is complete, finish by knitting one rnd in MC.
Knit up another cuff and enjoy cozy arms and wrists this fall and winter!
< Previous Project 9 – Knitted Cuffs, Shell Pattern, Take Two!


text:
Зоркин:
 Зоркин, Никита Владимирович (род. 2000) — российский хоккеист.
 Зоркин, Тимофей Васильевич (1904—1965) — советский хозяйственный, государственный и политический деятель, Герой Социалистического Труда.

 Зоркина, Зоя Васильевна (род. 1928) — Герой Социалистического Труда.


Since the mid-20th century, developmentalists have researched how social deprivation within orphanages affects a child's ability to later form an attachment to his primary caregiver. John Bowlby's theory of attachment posits that children who do not develop any attachment style within the first two years of their life will subsequently never be to able to become attached to their primary caregivers. However, longitudinal studies conducted on children reared in orphanages have proved that there is no critical period within which attachment must be formed. A child's ability to form an attachment to his adoptive parent is not based on his age, but rather on the parent's commitment to promoting a secure attachment style through affectionate and responsive care.
Ariel Clemons is a freshman undergraduate student in the Peabody College majoring in Human and Organizational Development. Ariel is a native of Potomac, Maryland, and a member of Phi Sigma Pi National Honor Society. In addition, Ariel's paper "Female Submissiveness: The Inability to Escape Male Authority in Rebel Without a Cause and 'Daddy'" was selected for presentation during the Spring 2009 Vanderbilt Undergraduate Writing Symposium. Ariel hopes to continue developing her writing skills and style during the remainder of her undergraduate experience at Vanderbilt.
CLEMONS, Ariel Hilary. The Effects of Social Deprivation within Orphanages on Parent- Child Attachment: How Adoption can Ameliorate Attachment Problems. Vanderbilt Undergraduate Research Journal, [S.l.], v. 5, july 2009. ISSN 1555-788X. Available at: <http://vurj.vanderbilt.edu/index.php/vurj/article/view/2808>. Date accessed: 26 apr. 2019. doi: https://doi.org/10.15695/vurj.v5i0.2808.


Shopping around for an electric dog fence but not sure what features to look for?
Should I get a wireless or an in-ground fence? Which one is right for my dog's size and temperament? How many levels of static correction do I need?
The fact that these points surface over and over is a sure fire indicator that they're important in the buying process. Knowing the answers to these questions will help you make a more informed buying decision and ensure that you end up with a fence you're satisfied with.
Now — let's dig into the Top 10 things to look for when you're shopping for an electric dog fence.
1) How much area can it cover?
The transmitter is the component that determines how much area an electric fence can cover. While some transmitters can only cover 1 acre, others are powerful enough to cover 25 acres or more.
2) What's involved in the installation process?
Wireless systems are quick and easy to set up — you can easily have one up and running in less than an hour.
In-ground fences take more time and elbow grease to install. Depending on the area that needs to be covered you're looking at anywhere from 1-2 days.
One thing to keep in mind with either type of electronic pet containment system is that they can both be used in conjunction with an above ground fence. For example, many people stopped their dog from digging under or jumping over a wood or chain link fence by attaching their boundary wire to it.
3) What size dog can it be used on?
The receiver collar is without a doubt one of the most important things to consider when buying either type of electric dog fence.
How big is the receiver unit?
Although there are a huge variety of collars available that can be used on dogs from as small as 5 lbs all the way up to 250+ lbs, one of the things I want to caution you on is that you can't always trust the manufacturer's recommendation.
On more than a few occasions I found that what the manufacturer recommended was very different than what people using the system recommended.
For example, PetSafe says that their Stubborn Dog In-Ground Fence system is good for any dog over 8lbs. However, because the collar that comes with this fence is one of the largest and heaviest on the market the vast majority of consumer reviews suggest that most people are using it on dogs in the 50-200 lb range.
For this reason my comparison tables list the weight range that consumers suggest rather than what manufacturers recommend.
4) What features does the receiver collar have?
Is it waterproof? Waterproof implies that the collar can be submerged for prolonged lengths of time. Water resistant means that it's OK to get the collar wet — like if your dog is swimming or out in the rain — but submerging it for any length of time may damage it.
Is it durable? Only you know how rough and tumble your dog likes to play so whether or not the collar will hold up to whatever your dog puts it through is definitely something you want to take into consideration when comparing one system to another.
Rechargeable vs disposable batteries: Some of the things to think about when dealing with rechargeable batteries are: How often will the collar need to be recharged? How long does it take to recharge? Is the charger included with the fence kit or does it have to be purchased separately?
In addition to knowing about how often the battery has to be changed, when you're dealing with disposable batteries it's also important to know if they're proprietary or non-proprietary. Proprietary batteries are generally more expensive be harder to find whereas non-proprietary batteries are cheaper and can be found pretty much anywhere batteries are sold.
Does it have a safety time out? Most collars have some kind of built in safety time out that will ensure your dog never receives an electric stimulation for longer than a set amount of time.
But every collar is different: some automatically shut off after 30 seconds, others after a minute. Some deliver a continual stimulation until they time out, others pulse on and off in cycles of stimulation and rest.
However the collar functions in this regard, for your pet's protection it's best to be sure it has some sort of safety feature that will ensure the static correction automatically turns off after a certain period of time.
Does it have a low battery warning? Whether you're dealing with rechargeable or disposable batteries, most people feel it's important to have some kind of audible or visual warning to alert you to a low battery.
Are other collars compatible with the system? This is especially important if yours is a multiple dog household. Being able to choose collars that match the size and temperament of each dog plays an integral role in keeping all your canine buddies safe and happy.
5) How many levels of static correction are there?
Although many people still use the term 'shock collar', it's an outdated term that was used in reference to collars made decades ago. These collars were very powerful, had few levels of static correction to choose from and had few safety features.
Today's modern electronic collars are much safer and have built in safety features that will prevent your dog from getting hurt. Despite that, there's always going to be a lot of controversy surrounding the use of e-collars.
No matter what term you use, the static correction is what every collar on every electric fence system uses to train any dog so no matter what fence you buy, you can't get around the fact that at some point your dog's going to receive an electric stimulation.
Are they adjustable? Whether your dog is big or small, compliant or stubborn, you want to be able to adjust the intensity level of their static correction so that you can get maximum results with the absolute minimum amount of electric stimulation.
Is there a beep (or beep and vibrate) only training mode? Most collars on the market today offer a beep or beep and vibrate only warning mode which allows you to familiarize your dog with their new boundaries before introducing the static correction.
By training your dog in this manner the warning quickly becomes the only motivation they need to stay within the boundaries of their containment area.
6) How reliable is it?
This one is tough question to answer in a few sentences but it's definitely something you need to consider when buying any type of electric dog fence.
What I can tell you is that I've done all the leg work when it comes to researching various electric fences and assessing the reliability of any given system is one of the things I've included in the in-depth reviews I've written.
So before you buy you might want to check out my comparison tables to learn more about the differences between various in-ground and wireless fences.
There are a lot of things that factor into cost when you're looking at electric dog fences. Things like what comes in the kit? What items will you need to purchase separately? So when it comes to price I really can't give you a 'normal' or 'average'.
You can get a reliable basic in-ground fence system for around $100 or you can pay upwards of $400 for a system with a lot more features and all the bells and whistles.
There are DIY dog fences out there for all different sizes and shapes of yards and for every size and temperament of dog. What's important is that you take the time to look around and figure out which one is the best for you and your furry friend.
Because there are so many things to consider I've written a separate article that will help you estimate how much you'll spend on your fence, depending on your situation.
Having said all that, what I can say for sure is that almost everyone agreed that buying an electric dog fence is less about the price and more about having a system that keeps their dog safe and secure no matter what type of property they live on or what type dog they have.
8) Can I have multiple dogs on the system?
Is there a limit to the number of dogs you can have on the system? Most systems allow an unlimited number of dogs as long as they each have their own receiver collar but if you have more than one dog, you'll want to double check to ensure the fence you buy can accommodate all your four legged friends.
Are there compatible collars for different size dogs? If your multiple dog household is of the Mutt and Jeff variety, you'll need to be sure that the system you end up with has compatible collars for all different size dogs.
Can you set the correction level of each collar individually? Because every dog has a different personality and temperament, it's important to be able to tailor the static correction level on each collar to the needs of each individual dog.
For example, your easy to train dog probably won't need the same intensity level as your hardheaded buddy.
9) Does it come with battery backup and a surge protector?
Consumer reviews indicate that these are the 2 most important components when it comes to keeping your fence up and running in the event of a power outage or lightning strike.
Battery backup: Whether you decide to go with a wireless or in-ground fence your transmitter will need to be plugged into a standard outlet to work. And unless you have a battery backup, if the power goes out your fence stops working and your dog will be left unprotected.
In the event of a power outage an Uninterruptible Power Supply, aka UPS, can provide your transmitter with battery backup and keep your fence up and running for a limited amount of time.
Some systems come with a battery backup but if you're buying one that doesn't, depending on your situation you might want to consider adding a UPS to your list.
Surge protector: This device is only relevant if you end up with an in-ground fence. It's designed to protect your system from damage that can be caused by lightning-induced power surges that travel back up the boundary wire and damage your transmitter.
But you can't. Surge protectors for in-ground fences are specially designed to have ports on the bottom so that you can plug your boundary wire in and this is another item you might want to add to your list if it's not included in the fence kit you're buying.
10) How much ongoing maintenance will I have to do?
Like many electronic items, both wireless and in-ground fences have ongoing maintenance.
But without a doubt the top contender in this category is finding and repairing breaks in your boundary wire. This is by far the biggest hassle consumers wrote about in their reviews of in-ground dog fences.
Having said that you should also know that most people think it's well worth it. The time and effort they spend maintaining their in-ground fence is a small price to pay for the flexibility it offers them.
So there you have it…the Top 10 things to consider before buying an electric dog fence.
But probably one of the most important things to understand before you buy an electric dog fence is whether you'd be better off with a wireless or in-ground fence. There's a lot to that issue and knowing the 5 main differences between the two will help you decide which type is right for your situation.
That one's easy 😉 Just head on over to my Comparison page where you'll find links to reviews on different brands of electric dog fences.
I've done the research, I've left no stone unturned…and you'll get all the information you need in my in-depth reviews!


The Golden State leads the world in technology, but is hardly a model in handling its own water resources.
By now, many Californians are seasoned in the skills of household water conservation. Deep into a fourth year of drought, we have let our lawns turn brown and we're taking shorter showers. The state's water leaders are addressing the challenge with water cutbacks in cities, planning desalination and wastewater recycling plants, and ramping up a program to improve groundwater management.
But California is behind the global curve when it comes to building and operating reliable water supply systems.
"Everything that you can do wrong [in managing water] has been done in California," says David Zetland, a water policy author and assistant professor of economics at the Leiden University College in the Netherlands (and also on the Water Deeply board of advisors). Rivers have been drained to support cities and farms in the desert, he said. Groundwater use is entirely untracked. And state officials have allocated more water from California's rivers and streams than actually exists.
Other nations, stressed by their own water supply issues, have meanwhile emerged as leaders in an arena where California must now play catch-up. About a third of Singapore's water is provided by sewage treatment plants. Israel has dealt with intense drought by investing heavily in desalination plants and water recycling. Australia and Chile are leaders of sustainable agricultural water management, largely via sophisticated water markets.
One of the biggest flaws in California's water system is that the state does not manage groundwater use. Aquifers are a free-for-all where anyone with a well can withdraw all the water they want. As a result, groundwater reserves are shrinking – so dramatically that the Earth surface in parts of the Central Valley is subsiding by 2 inches per month, causing roads and canals to buckle and resulting in permanent loss of groundwater storage space as deep soil layers collapse.
California's environmental regulations are showing their weaknesses, too, as imperiled fish species – including Chinook salmon – are pushed toward the brink in the Sacramento-San Joaquin Delta. There, demand for water has had particularly visible effects on fish populations; species extinction is a real possibility as the drought continues.
Solving California's water woes could be done, many water policy analysts say, by implementing a water market, where users pay a market rate, without subsidies, for every drop they use. Under the state's current system, the biggest users – such as corporate farms – often pay the least for water, with users on municipal systems paying vastly more. Direct comparisons are tricky, because urban water systems require more expensive infrastructure. But to put it differently, the present system is like charging higher gasoline prices to drivers of fuel-efficient cars and offering discount rates to drivers of gas guzzlers.
Reversing this subsidized water supply system would create incentive for urban and agricultural users to conserve water. Farmers in a water market system would give more consideration to what crops they are growing and where, and many growers might abandon especially arid regions, where irrigation needs are greater.
Lester Snow, former director of the California Department of Water Resources and also former secretary of the state Natural Resources Agency, stresses such a system would have to be fair.
Workers move a pipe at the Carlsbad desalination facility under construction in San Diego County. In the background are thousands of reverse osmosis vessels that will extract the salt from seawater. When finished this fall, the plant will be operated by an Israeli contractor, because California lacks the expertise in its own workforce. Associated Press photo by Gregory Bull.
Another prerequisite for a functioning water market is that groundwater use must be managed and tracked just as surface water is. Otherwise, Snow cautions, a system that encourages buying and selling of water would accelerate a practice known as groundwater transfers, or substitutions, whereby farmers sell their surface water and then irrigate their own crops by simply pumping more groundwater.
The water market of Australia, a nation plagued by chronic drought, has become a model of efficiency. Mike Young, professor of water and environmental policy at the University of Adelaide, says the nation made "massive mistakes" in the handling of its water.
"Some of the things that went wrong were not managing our groundwater properly and not understanding the link between ground and surface water," Young says.
In many situations, groundwater is just the subsurface extension of a river or lake. This means it is ineffective to restrict direct pumping from the surface supply if you also continue to allow unrestricted pumping from nearby wells – as California does.
Over a period of several years, says Young, Australia's water management system was overhauled and is now considered one of the most lauded in the world.
"Water is handled like money," Young says. "Everyone has a water account, almost like a bank account." Registered permit holders can buy and trade water as shares, with all transactions carefully tracked. Caps on surface and groundwater use are also firmly enforced to protect baseline environmental needs.
"Anyone who takes water without a water right has the books thrown at them, and we have water bailiffs going around continuously to make sure people are complying," Young says. "Farmers understand that if someone is taking water without an allocation, they're stealing from their neighbors." The system also prompted farmers to change how they operate and what they grow, Young says.
United States leaders have taken note of other nations' efficiency in water management. Nevada recently called on Young to counsel the desert state in drought adaptation strategies. In June, California hosted several Israeli water experts in Sacramento to offer guidance on the Golden State's water crisis. Californians have also gone abroad seeking ideas.
Dave Feldman, a professor at U.C. Irvine's School of Social Ecology, has visited Melbourne, Australia, three times in the past two years with a group of colleagues and students to study the way cities use and handle water, and to explore whether these practices could be imported to the U.S.
Feldman says Australian urbanites have adapted to drought in rather simple ways.
"Most of the changes that have been made in Australia regarding water and managing the drought have been behavioral changes, not so much technological changes, or economic changes," he says.
Feldman observed widespread use of water recycling programs, gray-water recapture for irrigation purposes, rain catchment and storage systems. Wetlands have also been preserved as biofilters for stormwater runoff.
Feldman says there are barriers – he calls them "societal apprehensions" – that could keep these ideas from rooting in the U.S. For example, using recycled gray water to irrigate lawns or installing rainwater storage tanks creates liability risks if people drink the water – risks Australians as a culture have learned to accept in a way Americans have not.
Snow says the U.S., and especially California, shouldn't necessarily need to look overseas for innovative approaches to drought adaptation.
"All the best solutions are already happening in parts of California," Snow says. "What we have to do is just get those solutions to scale." He says gray-water reuse, wastewater recapture and recycling, and the flooding of agricultural land to recharge groundwater all exist now in California and should be practiced more widely.
Other countries, he adds, are not more innovative; they have simply employed their innovations more efficiently than California has.
Australian wineries have done this in part by optimizing the way facilities operate. In particular, they are adept at capturing and reusing water – mostly for cleaning equipment – multiple times before it goes down the drain. Israel has done this by embracing seawater desalination, which now meets about half the nation's water needs. Recycled urban wastewater meets much of Israel's agricultural needs.
The United States lags in water recycling, reclaiming and treating less than 1 percent of all urban wastewater.
California is only beginning to test the waters of desalination. A new plant in Carlsbad, in San Diego County, took three years and a billion dollars to construct. Yet it will be managed initially by an Israeli company – IDE Technologies – because sufficient expertise doesn't exist yet in the California workforce. When it finally goes online this fall, it will pump enough fresh water into a 10-mile pipeline to support the daily water needs of 300,000 people.
But not everyone believes desalination is the answer to California's water woes.
"Desal is not a panacea," Snow says. Rather, he characterizes desalination plants as "boutique" solutions – technology that may work in some locations but which, if built everywhere, would cause more problems than it solves.
The biggest drawbacks of desalination plants are the cost of building them and their intensive energy demands. Zetland is among those who think desalination is a counterproductive measure. He says the Carlsbad plant could simply not have been built at all if the region's users just consumed less water.
Mike Lee, public affairs officer with the San Diego County Water Authority, says the region has already made substantial cutbacks in potable water use. But the locals who will soon drink that desalinated water still consume about 150 gallons per person per day – two or three times as much as people in parts of northern Europe, Australia and even Northern California.
"In San Diego, they need the desalinated water, for what – to water their lawns?" Zetland says.
The real irony of the Carlsbad desalination plant, Zetland adds, is that its cost is being distributed across three million rate payers, not just the people receiving its water. It's a technique called postage stamp pricing, he said, that effectively hides the cost. "If they charged people the actual price of the desalinated water, people would use so much less water that they wouldn't even need the desalinated water," Zetland says.
Not all drought-stressed nations have excelled past California in conservation and efficiency. Spain and Saudi Arabia have both overplanted crops in regions with inadequate surface water supplies, driving overdrafting of groundwater – exactly what California has done. China is voraciously consuming its water resources. The developing super-economy is now damming and diverting rivers at an alarming rate. Roughly half the world's dams have been built in China, and plans are unrolling to build many more.
California, Snow says, is lagging for no reason except that the state is relatively young and has not, until now, felt the pressures that Australia and the Middle East have.
California happens to be located at a very unique convergence of latitude, ocean currents and geological structures that have made it possible to develop a major economy in an arid land. Large rivers run through deserts in California, and some of the highest mountains on the continent loom over some of the most arid valleys, their peaks buried most years in snow.
But that easy availability of water, at least for now, is gone.
Alastair Bland is a freelance journalist in San Francisco, CA. He can be reached at allybland79@gmail.com or via Twitter at @allybland.
Top Photo: Jorge Vargas, a foreman for Maggiora Brothers Drilling Inc., poses for a photograph while drilling an 800-foot-deep water well at an almond farm in Chowchilla, California, on Friday, April 4, 2014. In California's drought, well drillers are experiencing a boom in business because farmers are relying more on groundwater to irrigate their crops (by Scott Smith, Associated Press).


text:
» Łukasz Dudek
Łukasz Dudek
He's been climbing since 1999. At first, apart from rock climbing, he also concentrated on national and international competitions. Since 2009, he's completed almost 20 routes at 9a. Among his achievements, there's also a boulder called Obsesja rated 8c that he's the author of.
He took his first steps in multi-pitch climbing in the mountains together with Jacek Matuszek that he created the Alpine Wall Tour project with. As part of this project, he sent, among others, End of Slience 8b+, Des Kaisers Neue Kleider 8b+, Silbergeier 8b+, Bellavista 8b+, Project fear 8c, Spanish route 8b+, I Premiere 7b (a new route at Cima Grande). In 2019, he went one step further and completed the first ascent of an 8-pitch route Tortour 8c in the rope solo style.
On August 8th that same year, after 17 hours of rope soloing, he reached the top of Cima Ovest thus becoming the first man to climb Pan Aroma 8c alone.


text:
Celyphus hyalinus är en tvåvingeart som beskrevs av Karsch 1884. Celyphus hyalinus ingår i släktet Celyphus och familjen Celyphidae.

Artens utbredningsområde är Sri Lanka. Inga underarter finns listade i Catalogue of Life.

Källor

Tvåvingar
hyalinus


Pregnancy conjures up a happy image of feet propped up with a pint of ice cream, along with a side of pickles. While it is true that you are eating for two, make sure what you are putting into your body is as nourishing for you as it is for the baby.
Chances are, you will experience some pretty intense hunger hankerings; cravings can, however, signal a lack in your diet. If you understand the trigger then you have a better chance of making healthier choices. By starting your day with a hearty breakfast, you are likely to be more discerning throughout the day.
If you are suffering from nausea, try a freshly pressed juice or smoothie, which will make it a lot easier to consume your fruits and veggies. A green smoothie or juice can actually nip many cravings in the bud, and you are consuming a majority of your nutrients for the day in one serving! Lemon water is a great way to stay hydrated, which as we know, is very important.
Avoid eating out of desperation by keeping your refrigerator and pantry stocked well with fruits, veggies, and whole grains.


text:
UN donates telemedicine devices to boost healthcare services in Somalia
Several hospitals and health clinics in Somalia are being equipped to strengthen their capacity to provide healthcare services, thanks to an innovative telemedicine project by the Ministry of Health and Human Services (MoH) supported by the International Organization for Migration (IOM).
IOM, through funding from the multi-donor Somalia Humanitarian Fund (SHF), handed over digital devices and office equipment to the MoH in Somalia on Thursday (January 7) to support the introduction of telemedicine in Somalia's health system. The donation includes screens, video cameras, a PC, video conference equipment and 50 iPads.
Somalia's health system has been significantly damaged by years of conflict and recurrent humanitarian crisis, and most of the health care workers working on the frontlines against COVID-19 and other disease of epidemic potential have limited expertise and experience of treating critically ill patients.
The new telemedicine project aims to setup the necessary facilities to enable these local medical professionals to access a growing body of health knowledge and expertise inside and outside the country. Knowledge-transfer resulting from this project will pave the way to revolutionizing the Somalia healthcare system through a systematic knowledge-transfer to improve healthcare service provision in the country.
IOM has been supporting health capacity injection through IOM's Migration for Development in Africa (MIDA) programme, by placing diaspora health experts in hospitals and clinics throughout Somalia. Due to the current COVID-19 situation, it has been increasingly difficult to recruit senior health care workers to respond to the urgent demand of expertise to address the COVID-19 pandemic.
"This project will link doctors in Somalia with experts abroad and in other parts of the country to complement the diaspora programme which physically places diaspora doctors in the country," explained Kerry Kyaa, IOM's Senior Health expert.
"Telemedicine will also mitigate the limitations placed by COVID-19 on international travel and physical distancing."
Expert doctors will help those on the frontlines with clinical diagnosis and will give real time recommendations for patient management and reduce morbidity and mortality. This will be achieved through the setup of collaboration systems to facilitate videoconferencing and teleconsultations
During the handover ceremony, Somalia's Minister of Health and Human Services, HE. Dr. Fawziya Abikar Nur, said
"I would like to thank IOM on behalf of the Ministry of Health and the people in Somalia. IOM has done a great job with the ministry of health before during, and after COVID-19. This telemedicine project is very crucial for the health sector and the people in Somalia will benefit immensely from it."
"IOM is proud to be supporting Somalia with this new ambitious telemedicine programme and shall continue to work with MoH and partners to ensure that migrants and displaced populations can have access to a free and better health care," said Richard Danziger, IOM Somalia Chief of Mission.


text:
\section{\label{introduction}Introduction}
Topological insulators are a new state of electron matter that have attracted enormous interest recently \cite{TIreviews}. Similar to the integer quantum Hall effect, these states can be distinguished from conventional insulators by topological invariants and robust sub-gap surface states. Topological band insulators cannot be continuously deformed into a topologically trivial state without closing the band gap.

In two spatial dimensions and in the presence of time-reversal symmetry, topological insulators are characterized as quantum spin Hall (QSH) states \cite{TIreviews}. If the component of the electron spin along a certain quantization axis is conserved, the picture of the QSH state is especially simple. Then, the currents in the edge states cause opposite Hall conductivities for spin up and spin down, respectively, which results in quantized spin-Hall transport, with the conductance determined by a topological quantum number per spin obtained from the bulk band structure. This simple QSH state can be viewed as two copies of Haldane's 1988 quantum Hall state without net magnetic field \cite{haldane}, with the two copies being related to each other by time reversal. In the case of broken time-reversal symmetry, e.g., if one leaves out one copy or reverts its orbital part, one obtains a related state, known as quantum anomalous Hall (QAH) state.  This state exhibits a quantized charge Hall conductance at zero external magnetic field (see, e.g. Ref. \cite{QiPRB2006}), as in Haldane's initial proposal for the spinless model. In both, QSH and QAH,  the occurrence of edge states through which the electrons propagate comes as a direct consequence of the topologically nontrivial nature of the bulk electronic band structure \cite{TIreviews}.

Usually, this topological structure of the band structure state is caused by the presence of spin orbit coupling. Initially, Kane and Mele proposed a spin-orbit term on the graphene lattice \cite{kanemele}, but it turned out that  for graphene, the effect would be too weak \cite{yao,fabian}. Based on an insightful theoretical proposal \cite{bernevig}, the QSH state could instead be realized in HgTe/CdTe quantum wells, where hallmarks of the QSH effect could be experimentally observed the first time \cite{konig,TIreviews}.

All this beautiful physics can be understood in the single-particle picture. One could ask, however, if similar topologically non-trivial states can arise from interactions, through a phase transition at some critical temperature. Following this idea, different simple models were analyzed.  Raghu 	\textit{et al.} \cite {raghu} considered the honeycomb lattice with strong next-nearest neighbor repulsion using mean-field and functional renormalization group (fRG) techniques. Above a nonzero critical interaction strength \cite{raghu}, the quantum-spin Hall state was found as the ground state of the system. This instability implies  a spontaneous breaking of the spin rotational invariance. While this study serves as a proof of principle, it is by no means clear how one can realize the rather peculiar interaction with strong second nearest neighbor repulsion. Another study was performed by Zhang \textit{et al.} \cite{3DTMI} for a three-dimensional lattice model where third-nearest neighbor interactions were essential to stabilize the QSH state.  A promising proposal came from Sun \textit{et al.} \cite{sun} who argued, based on mean-field calculations, that quadratic band crossing point (QBCP) models should host QSH states already at arbitrarily weak interactions. The difference to the honeycomb lattice with its Dirac points is that, for a QBCP, the density of states is nonzero at the crossing point, and, hence already a small interaction suffices to drive an instability. This picture is also supported by a mean-field study of Wen \textit{et al.} \cite{ruegg} who found topologically non-trivial phases already for small interactions in Kagome and decorated honeycomb lattice models with quadratic band crossing points.

In this work we consider certain QBCP models \cite{sun} in two dimensions using fRG methods. This allows us to explore the possibilities for interaction-driven topological states beyond mean-field theory. We furthermore investigate if there can be superconducting states emerging from topologically non-trivial insulators.

We briefly note that these interaction-driven topological insulators are also referred to as {\em topological Mott insulators}. The same term is sometimes used in the study of a slightly different question, which is the interplay between a Kane-Mele spin-orbit term leading to a topological band insulator and the Hubbard onsite interaction leading to a Mott insulator, if sufficiently strong \cite{rachel,hohenadler}. Our paper addresses the interaction-induced generation of a Kane-Mele-type term in absence of significant spin-orbit coupling in the bare Hamiltonian, by interactions that are weaker than those required to drive the system Mott-insulating.  A recent work \cite{varney} addresses the transition between topologically non-trivial and trivial states when nonzero interaction parameters are changed in finite-size systems. Interestingly, the single-particle gap can remain robust across the topological transition, and both sides of the transition are insulators.

\section{Continuum fermion model}
\label{continuum model}
We first consider a spin-$1/2$ model in the continuum in two dimensions, which describes the neighborhood of the QBCP in a quite general way. Following Ref. \cite{sun} let the Hamiltonian be given by
\begin{equation}
H=H_{\text{free}}+H_{\text{int}},
\end{equation}
where the free part reads as
\begin{eqnarray}
\label{hfree}
H_{\text{free}}&=&\sum_{o,o',s} \int d \mathbf{k}\medspace \psi^\dagger_{o,s}(\mathbf{k}) H^0_{oo',s} (\mathbf{k}) \psi_{o',s}(\mathbf{k}) \nonumber \\
&=& \int d \mathbf{k}\medspace \Psi^{\dagger}(\mathbf{k}) \mathbf{H}^0 (\mathbf{k}) \Psi(\mathbf{k}).
\end{eqnarray}
Here the index $s$ denotes spin and $o=1,2$ denotes two different Fermi fields, which should be identified with the orbital degree of freedom. In the second line we have written the Hamiltonian in matrix notation so that $\Psi=(\psi_{A,\uparrow}, \psi_{B,\uparrow},\psi_{A,\downarrow},\psi_{B,\downarrow})^T$ and $\Psi^\dagger=(\psi^\dagger_{A,\uparrow}, \psi^\dagger_{B,\uparrow},\psi^\dagger_{A,\downarrow},\psi^\dagger_{B,\downarrow})$ combines spin and orbital degrees of freedom. We choose the free part to be of the form
\begin{equation}
\label{h0}
\mathbf{H}^0(\mathbf{k})= I_S \otimes  \left[d_I (\mathbf{k}) I+d_x (\mathbf{k}) \sigma_x+d_z (\mathbf{k}) \sigma_z \right] \, ,
\end{equation}
where $I_S$ is the unity matrix in spin space, I the unity matrix in orbital space, and $\sigma_x$ and $\sigma_z$ the Pauli-matrices. The integral is over a disk in two-dimensional momentum space. The disk radius, i.e. the ultraviolet (UV) cutoff, just determines the energy window focused on and will not be of any qualitative importance.
The coefficients are $d_I(\mathbf{k})=t_I(k_x^2+k_y^2)-\mu$, $d_x(\mathbf{k})=2 t_x k_x k_y$ and $d_z(\mathbf{k}) =t_z(k_x^2-k_y^2)$. Usually, we will set $t_I$ to zero and $t_x=t_z=t$ for simplicity.  There is no $t_y$  as this would break time-reversal symmetry or already create a QSH state at the bare level. Except for Sec. \ref{sc}, the chemical potential is set to zero so that the QBCP lies at the Fermi level. Note that we exclude the possibility of spin orbit coupling by restricting the Hamiltonian to unity in spin space.

The free part can be easily written in a diagonal basis. With a proper transformation of the Fermi fields $\gamma_{n,s}(\mathbf{k})=\sum_{o} u_{n,o}(\mathbf{k}) \psi_{o,s}(\mathbf{k})$, where $\gamma_{n,s}$ is the transformed field in band $n$ with spin $s$, the free Hamiltonian becomes
\begin{equation}
\label{freediag}
\mathbf{H}^0 (\mathbf{k})=I_S \otimes \left[ d_I (\mathbf{k}) I+d_z' (\mathbf{k}) \sigma_z \right]  ,
\end{equation}
with $d_z'=\sqrt{d_x^2+d_z^2}$. The band structure of the model consists of two parabolas, which have a QBCP at the origin (see Fig. \ref{continuumplot}). In our choice $t_x=t_z=t$, the dispersion is rotationally invariant in the plane.

The interacting part of the Hamiltonian contains local intra- and interorbital repulsions,
\begin{widetext}
\begin{eqnarray}
H_{\text{int}} & = &\frac{U}{2} \sum_{o,s\ne s'} \int d\mathbf{k} d\mathbf{k'} d\mathbf{q}\, \psi^\dagger_{o,s}(\mathbf{k}) \psi^\dagger_{o,s'}(\mathbf{k'})\psi_{o,s'}(\mathbf{k'}-\mathbf{q})\psi_{o,s}(\mathbf{k}+\mathbf{q})\notag\\
&&+\frac{U'}{2} \sum_{o \ne o',s,s'} \int d\mathbf{k}d\mathbf{k'} d\mathbf{q} \medspace  \psi^\dagger_{o,s}(\mathbf{k}) \psi^\dagger_{o',s'}(\mathbf{k'})\psi_{o',s'}(\mathbf{k'}-\mathbf{q})\psi_{o,s}(\mathbf{k}+\mathbf{q}) \notag\\
&=& \sum_{o_1,o_2,o_3,o_4 \atop s,s'} \int d\mathbf{k}_1 d\mathbf{k}_2 d\mathbf{k}_3 d\mathbf{k}_4\,
V_{o_1 o_2 o_3 o_4}( \mathbf{k}_1,\mathbf{k}_2,\mathbf{k}_3,\mathbf{k}_4) \psi^\dagger_{o_3,s}(\mathbf{k}_3)\psi^\dagger_{o_4,s'}(\mathbf{k}_4 )\psi_{o_2,s'}(\mathbf{k}_2)\psi_{o_1,s}(\mathbf{k}_1) \, .
\label{H_int}
\end{eqnarray}
\end{widetext}
If we use the basis in which the free Hamiltonian is diagonal, we have to transform the interacting part of the Hamiltonian accordingly:
\begin{align}
&\lefteqn{V_{n_1 n_2 n_3 n_4}( \mathbf{k}_1,\mathbf{k}_2,\mathbf{k}_3,\mathbf{k}_4)} \notag\\
&= \sum_{o_1,o_2,o_3,o_4} V_{o_1 o_2 o_3 o_4}( \mathbf{k}_1,\mathbf{k}_2,\mathbf{k}_3,\mathbf{k}_4) \notag
\end{align}
\begin{equation}
\times \quad u_{n_1 o_1}(\mathbf{k}_1) u_{n_2 o_2}(\mathbf{k}_2) u^*_{n_3 o_3}(\mathbf{k}_3) u^*_{n_4 o_4}(\mathbf{k}_4)  \label{omakeup}
\end{equation}
so that the local interaction (\ref{H_int}) assumes a pronounced momentum dependence in the new basis. The prefactor consisting of the four $  u_{n o}(\mathbf{k})$s is sometimes referred to as orbital make-up.

As pointed out in Ref. \cite{sun},  the QBCP carries a vortex-like winding of the Bloch eigenvectors (with two components for the amplitudes in the two orbitals) that cannot be made undone continuously. The core of the vortex needs to be a degeneracy point, and hence the QBCP cannot be removed easily. When we think about the stability of the QBCP with respect to interactions, there are essentially two ways to remove the QBCP which we will find to be realized depending on the interaction parameters. The free Hamiltonian has rotational invariance in the $k_x$, $k_y$-plane. One way is now to break this rotational symmetry by splitting the QBCP into two Dirac points. In terms of the eigenvectors this stretches out the winding along a branch cut connecting the two Dirac points with an inversion of the direction of the Bloch eigenvectors. The other way is to open a gap by breaking either time reversal symmetry in a given spin sector. This corresponds to a nonzero $d_y$-term.
Only when the $d_y$s in  spin-up and spin-down sectors are opposite in sign but of the same magnitude, time-reversal symmetry is still present. This state is then a QSH state. Otherwise, time-reversal symmetry is broken. If $d_y$ is spin-independent, we have a QAH state.

Next we study the instabilities of a continuum QBCP model and of a related lattice variant in the spin-$1/2$ case by a fRG approach. This extends the mean-field study of Sun \textit{et al.} \cite{sun} of a spinless model. We find that a single QBCP might be the most favorable situation to realize spontaneous QSH instabilities.  Compared to the previous studies neither particular longer-ranged nor rather strong interactions are needed, and no threshold value for the interaction strength needs to be exceeded.

\section{Functional Renormalization Group treatment}
In this section we describe the momentum cutoff fRG method \cite{hsfr,metzner,rgbook}, which is employed in this work.
We consider the action with fermionic Grassmann fields ${\gamma}_s(p)$ and $\bar{\gamma}_s(p)$,
\begin{align}
S(\gamma, \bar{\gamma})=&\int dp \,  \bar{\gamma}_s(p) Q^\Lambda(p) \gamma(p)\notag\\
&+\frac{T}{2} \sum_{s,s'} \int dp_1  dp_2 dp_3 \sum_{n_4} \, V(p_1,p_2,p_3,n_4)\notag\\& \times \bar{\gamma}_s(p_3) \bar{\gamma}_{s'}(p_4) \gamma_{s'}(p_2) \gamma_s(p_1),
\end{align}
where we used the combined index $p=(\mathbf{k};\omega; n)$ with the Matsubara frequency $\omega$, the band index $n$ as above and $\int dp= \Omega^{-1} \int d\mathbf{k} \sum_{\omega,n}$. $s= \pm \frac{1}{2} $ is the spin projection. $\Omega$ is the Brillouin zone volume, or the considered volume in momentum space.
In the second term, the interaction, we have used wavevector-frequency conservation, and it is only summed over the fourth band index $n_4$.

The idea of the fRG method is to let the quadratic part of the action depend on a cutoff parameter, so that
\begin{equation}
Q^\Lambda(p)= \left[ C^\Lambda(\mathbf{k},n) \right]^{-1} \,  \left[ - i \omega+\epsilon(\mathbf{k},n) \right]
\end{equation}
with the dispersion $\epsilon(\mathbf{k},n=1,2)=d_I (\mathbf{k}) \pm d_z' (\mathbf{k})$ according to Eq. (\ref{freediag}). For the cutoff-function $C^\Lambda(\mathbf{k},n)$ we choose
\begin{equation}
C^\Lambda(\mathbf{k},n)=\Theta(|\epsilon(\mathbf{k},n)|-\Lambda).
\end{equation}
$\Theta$ is a step function, which is slightly softened in the numerical implementation. With this choice the modes with energy below $\Lambda$ are cut off, so that the free propagator $G^\Lambda_0(p) = - \left[ Q^\Lambda(p)\right]^{-1}$  is restricted to the high energy degrees of freedom.  At $\Lambda=\Lambda_0$ larger than the band width all perturbative corrections are set to zero, as all internal lines in the corresponding diagrams vanish. Hence the correlations and vertex functions of the theory at $\Lambda_0$ are precisely known. The fRG flow from $\Lambda =\Lambda_0$ down to lower $\Lambda$ provides the change of these functions, when the perturbative corrections are successively added to the system.
At $\Lambda=0$ the full action would be recovered, but in the cases and approximations below, the flow of some correlation or vertex functions, in part corresponding to effective interactions, diverge before at a critical scale $\Lambda_c$. This flow to strong coupling is indicative for a change of the ground state. The basic aim of the fRG flows used here is to find out which classes of vertex functions or effective interactions drive this flow to strong coupling.
From this we obtain tentative ground state diagrams, as described in the sections on the results. We note that the flows to strong coupling are to large extent physically meaningful artefacts of the approximations employed here. If the flow of the fermionic self-energy was included, a gap would open at the instability scale. This would regularize the divergence at nonzero scale. Unfortunately, such flows into the symmetry-broken or massive sector are by far more complicated when the competition of various instabilities or fermionic gaps is kept (which is our goal here). It gets more feasible when only one type of fermion gap is considered \cite{gapflow}. A recent work by Sinner and Ziegler \cite{sinner} shows how the functional RG in partially bosonized form (this formalism is e.g. reviewed in Ref. \cite{metzner}) can be used to determine the final interacting gaps in mono- and bilayer graphene with Coulomb interactions, when all modes are integrated out.

 The fRG flow for the vertex functions can be obtained from an exact flow equation for the generating functional of the one-particle irreducible correlation functions \cite{hsfr,metzner,wetterich}. This generating functional can be expanded in the fields, thus yielding an infinite hierarchy of integro-differential equations for the vertex functions. In order to apply the fRG method to our problem, we have to truncate the infinite system by setting the six-point vertex to zero. We also neglect the flow of the self-energy which will only become large, when the interactions flow to strong coupling. We then arrive at the fRG equations
for the coupling function $V^\Lambda ( p_1,p_2,p_3,n_4 )$, which in a spin-rotationally symmetric situation completely determines the interaction vertex. This equation reads as
\begin{align}
\label{dgl_v}
&\frac{d}{d\Lambda}V^\Lambda ( p_1,p_2,p_3,n_4 ) =\tau^\Lambda_{PP}+\tau^\Lambda_{PH,d}+ \tau^\Lambda_{PH,cr}\, ,
\end{align}
with the particle-particle channel
\begin{align}
\label{pp}
\tau^\Lambda_{PP}&( p_1,p_2,p_3,n_4 )=- T\int dp \sum_{n'} V^\Lambda ( p_1,p_2,p,n' )\notag\\
&\times L^\Lambda ( p,q_{PP} ) V^\Lambda ( p,q_{PP},p_3,n_4 ) \, ,
\end{align}
the direct particle-hole channel
\begin{align}
\tau&^\Lambda_{PH,d}( p_1,p_2,p_3,n_4) = -T \int dp \sum_{n'} \Bigl[-2V^\Lambda(p_1,p,p_3,n') \notag\\
&\times L^\Lambda(p,q_{PH,d} ) V^\Lambda(q_{PH,d},p_2,p,n_4) + V^\Lambda(p,p_1,p_3,n') \notag\\
&\times L^\Lambda(p,q_{PH,d} ) V^\Lambda(q_{PH,d},p_2,p,n_4) + V^\Lambda(p_1,p,p_3,n')\notag\\
&\times L^\Lambda(p,q_{PH,d} ) V^\Lambda(p_2,q_{PH,d},p,n_4)    \Bigr] \, , \label{phd}
\end{align}
and the crossed particle-hole channel
\begin{align}
\label{phcr}
\tau^\Lambda_{PH,cr}&( p_1,p_2,p_3,n_4 )= - T \int dp \sum_{n'} V^\Lambda(p,p_2,p_3,n')  \notag\\
&\times L^\Lambda(p,q_{PH,cr} ) V^\Lambda(p_1,q_{PH,cr},p,n_4)\, ,
\end{align}
where $q_{PP}=(-\mathbf{k}+\mathbf{k}_1+\mathbf{k}_2;-w+w_1+w_2;n')$, $q_{Ph,d}=(\mathbf{k}+\mathbf{k}_1-\mathbf{k}_3;w+w_1-w_3;n')$, $q_{Ph,cr}=(\mathbf{k}+\mathbf{k}_2-\mathbf{k}_3;w+w_2-w_3;n')$ are the quantum numbers of the second loop line, $p=(\mathbf{k};w;n)$ are those of the first line.
Note that we also have to sum over the band index $n'$ of the second internal line, whereas the momentum and frequency are fixed by conservation. The fourth momentum and frequency in the interaction vertex is fixed by conservation, so that here only the band index  is written.
The internal loop is given by
\begin{equation}
L^\Lambda(p,p')=S^\Lambda(p)G^\Lambda(p')+G^\Lambda(p)S^\Lambda(p')\, ,
\end{equation}
with the single-scale propagator
\begin{equation}
S^\Lambda(p)=G^\Lambda(p) \left( \frac{d}{d\Lambda}Q^\Lambda(p) \right) G^\Lambda(p)\, ,
\end{equation}
which has support only at the scale $\Lambda$, as the $\Lambda$-derivative of the cutoff-function is only nonzero there.
In our  approximation of neglecting self-energy corrections, the full propagator $G^\Lambda(p)$ is identical to the free propagator.

The frequency dependence of the vertex is ignored in this work, as we are mainly interested in low-frequency vertices that are relevant for static ordering. Thus the frequency summation in the fRG equation can be performed easily analytically. The integration over momentum space is done numerically. For this purpose we divide the momentum space in several patches and compute the coupling function only on a finite set of momenta on a ring around the QBCP, in analogy with previous $N$-patch fRG studies \cite{hsfr,honhon}. Thereby, the coupling function is set constant within each patch (see Fig. \ref{continuumplot}).
The advantage of setting the set of momenta on which the coupling function is computed on a ring is, that we can take into account the effect of orbital make up, i.e., the variation and winding of the Bloch functions around the QBCP. The Bloch functions enter the coupling function in band language via the orbital makeup in Eq. (\ref{omakeup}).
This variation can be important for the angular variation of gap structures \cite{honerkamp-epjb} and can certainly change the competition between different instabilities. We note that other RG studies \cite{vafek2010,vafekyang2010} of related problems with two QBCPs contract the wave-vector dependence directly to the Fermi point, i.e. form one big patch and parametrize the interaction by a handful of coupling constants $g$s for the scattering between the Fermi points. While we do not have evidence for a failure of this procedure for the QBCP model, in the iron pnictides, a similar approximation overlooks the angular gap structure \cite{honerkamp-epjb}, and, in principle, the contraction of a winding Bloch function on the center of the winding is ill-defined, at least for a subset of interaction processes.
Moreover, our more refined patching schemes allows us to study the doped case as well, where the Fermi surface is a small ring around the QBCP point.

We have checked that additional radial patches (i.e., introducing a second ring) do not change the qualitative results stated in this work.
Note that in the continuum the UV cutoff, i.e., the starting scale $\Lambda_0$,  is somewhat arbitrary. Therefore, we choose some fixed UV cutoff. The explicit calculations confirm the expectation that this choice only affects the absolute value of the critical scale, but not the type of instability.

\begin{figure}
\begin{center}
\includegraphics[scale=.3]{contdisp.eps}
\includegraphics[scale=.25]{patching.eps}
\end{center}
\caption{Left:  Dispersion relation of the continuum model with the QBCP. Right: Sketch of the patching-scheme: the central red dot is the QBCP, and the black dots denote the momentum vectors $\mathbf{k}$ associated with respective patch, for which the coupling function is computed.}
\label{continuumplot}
\end{figure}

\section{Emergent order parameters and phase diagram in the continuum model}
By investigating the fRG flow of the effective interaction for different ratios of $U$ and $U'$ for the QBCP at the Fermi level we usually encounter flows to strong coupling at some critical scale $\Lambda_c$.  The main growth is in particle-hole channels with zero momentum transfer, leading to very sharp structures in the effective interactions (see Fig. \ref{effww}). If we focus on this dominant zero-momentum transfer component and drop the remaining interaction terms, the effective interaction becomes infinite range in real space and decomposes into a product of two fermion bilinears, each with one creation and one annihilation operator at the same wave-vector. This interaction can then be solved in mean-field theory. Then, the bilinears correspond to order parameters of the strongly coupled phase, the emergence at low scales of which is indicated by the flow to strong coupling. In more detail, we find, depending on the interaction parameters, the following order parameters:
\begin{align}
\label{mfnematic}
&\vec{Q}_\text{SN}=\int d\mathbf{k} \langle \Psi^{\dagger}(\mathbf{k})(\vec{\tau} \otimes \sigma_z)\Psi(\mathbf{k})\rangle
  \\ &=\int d\mathbf{k} \sum_{s,s'}\langle \vec{\tau}_{s,s'} [\psi^{\dagger}_{A,s}(\mathbf{k}) \psi_{A,s'}(\mathbf{k})-\psi^{\dagger}_{B,s}(\mathbf{k}) \psi_{B,s'}(\mathbf{k})]\rangle \, ,\notag
\end{align}
\begin{align}
\label{mfqah}
&\Phi_{\text{QAH}} =\int d\mathbf{k} \langle \Psi^{\dagger}(\mathbf{k})(I \otimes \sigma_y)\Psi(\mathbf{k})\rangle  \\
&=\int d\mathbf{k} \sum_{s} \langle \medspace i \medspace [\psi^{\dagger}_{B,s}(\mathbf{k}) \psi_{A,s}(\mathbf{k}) - \psi^{\dagger}_{A,s}(\mathbf{k}) \psi_{B,s}(\mathbf{k})]\rangle \, ,\notag
\end{align}
\begin{align}
\label{mfqsh}
&\vec{\Phi}_{\text{QSH}} =\int  d\mathbf{k} \langle \Psi^{\dagger}(\mathbf{k})(\vec{\tau} \otimes \sigma_y)\Psi(\mathbf{k})\rangle   \\
&= \hspace{-0.1cm}\int \hspace{-0.1cm}d\mathbf{k} \sum_{s,s'}\langle \vec{\tau}_{s,s'} \medspace i \medspace[\psi^{\dagger}_{B,s}(\mathbf{k}) \psi_{A,s'}(\mathbf{k})-\psi^{\dagger}_{A,s}(\mathbf{k}) \psi_{B,s'}(\mathbf{k})]\rangle \, , \notag
\end{align}
where the brackets $\langle \ldots \rangle$ denote thermal averages.

Here $\vec{\tau} $ are the Pauli matrices in spin space. If we choose $\vec{\tau} $ in the $z$-direction, the state with non-vanishing $\vec{Q}_\text{SN}$ is characterized by a mean-field that is odd both in the two orbitals and in the spin projection along the $z$ axis. For a given spin component, the QBCP splits into two Dirac points, either along the $k_x$ axis or along the $k_y$ axis. For the opposite spin projection, the dispersion is rotated by $90 ^\circ$. The translational symmetry however remains conserved. Therefore this state exhibits spin nematic (SN) order.

The order parameter $\Phi_{\text{QAH}}$ describes a QAH phase, in which time reversal symmetry is broken. This state has a gapped bulk spectrum, as can be found out from adding the mean-field to the free Hamiltonian. The state then has a quantized Hall conductivity and topologically protected edge states, as can be understood, e.g. by computing the Hall conductivity from the skyrmion-number formula and by looking at finite systems in real space \cite{QiPRB2006}.

The QSH phase corresponds to the third order parameter $\vec{\Phi}_{\text{QSH}}$. This phase is also gapped and breaks spin rotational symmetry. It has helical edge states, which results in quantized spin Hall conductivity.

Now let us discuss the parameter regions where these orders emerge in the continuum model in more detail. When we run the fRG with the local interaction parameterized by $U$ and $U'$  as initial conditions, we find different effective interactions dominated by the three types of ordering listed above in Eqs. (\ref{mfnematic}), (\ref{mfqah}) and (\ref{mfqsh}) as a function of $U'/U$.
From analyzing which component of these three grows most strongly we can deduce a tentative phase diagram describing the leading ordering tendencies. Here, the critical scale $\Lambda_c$ serves as an (upper) estimate for possible ordering temperatures, or at least for the onset of strong correlations of the type indicated. Note that the question as to whether these orderings actually occur in true long-range form or are prohibited by, e.g., collective fluctuations is not answered in this fRG scheme. Nevertheless, the analysis is expected to give a realistic account of the dominant non-local correlations. Another interesting possibility would be that the single-particle Hamiltonian already contains small terms corresponding to the addressed mean fields, e.g., due to spin-orbit coupling, and that these terms then get strongly enhanced at low temperatures due to the interaction effects monitored by the fRG.

The phase diagram obtained for the QBCP model is shown in Fig. \ref{pd-continuum}. For small values of the interorbital repulsion $U'$ we encounter the SN phase with suggested order parameter (\ref{mfnematic}). For $U'\gtrsim U/2$ the QAH-order parameter (\ref{mfqah}) is leading and above  $U'\gtrsim 0.7 U$ the system is unstable toward the QSH-order (\ref{mfqsh}).

In Fig.  \ref{effww} we show a typical plot of the effective interaction at the critical scale in the QAH phase. One nicely observes the sharp momentum dependence of the $\mathbf{q}=0$-instability in the strong horizontal features. Note also the different sign of the couplings with $o_1=o_2$ and $o_1\ne o_2$ respectively. This reflects the fact that the expectation value of $\psi^{\dagger}_{A,s}(\mathbf{k}) \psi_{B,s}(\mathbf{k})$ is imaginary and thus shows that the corresponding QAH mean-field breaks time reversal symmetry. The less pronounced vertical features correspond to a tendency  toward the emergence of the SN phase, which is still present but weaker than the leading QAH instability.
The other instabilities can also be inferred from analyzing these snapshots of the fRG flow near the instability for different values of the interaction parameters.

Upon changing $U'/U$, $\Lambda_c$ does not decrease significantly between different phases. This suggests that there is no direct competition between the different tendencies, and the phase transitions are first order.

In order to answer the question as to whether there is a critical interaction strength needed for the emergence of long range order, we also investigated the critical scale in dependence of the bare coupling strength for fixed $U'/U$ in all three regimes. We observed that the couplings do indeed diverge down to an interaction strength of less then $U=2t$ for a bandwidth of $20t$. Although an arbitrary small interaction strength is not numerically accessible, we expect the instability to persist to infinitesimally small interaction.

\begin{figure}
\begin{center}
\includegraphics[scale=0.5]{pdcont.eps}
\end{center}
\caption{Tentative fRG phase diagram of the continuum model as a function of the interorbital interaction parameter $U'$ in units of the intraorbital repulsion. $\Lambda_c$ denotes the critical scale, defined as the scale at which the couplings exceeds three times the bandwidth, obtained with a fRG calculation using $N=48$ patches per band, upper cutoff $\Lambda_{\text{UV}}=10t$ and $U=8t$. }
\label{pd-continuum}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[scale=0.5]{effww1.eps}
\includegraphics[scale=0.5]{effww2.eps}
\end{center}
\caption{Effective interaction near the critical scale in the QAH phase. The angle $\phi_1$ ($\phi_2$) of the first (second) ingoing leg is plotted on the y (x) axis, with the discretization shown in Fig. \ref{continuumplot}. $\phi_3=\pi$ is kept fixed. In our convention the first and the third line have the same spin. The upper plot shows the vertices with the orbitals  $o_1=o_2$, $o_3=o_4 \ne o_1$, the lower plot shows the combination $o_1=o_4$, $o_2=o_3 \ne o_1$. The somewhat weaker vertical features at $\phi_2=\phi_3$  belong to remnants of the SN instability that is predominant at smaller $U'$.}
\label{effww}
\end{figure}

The conclusion we can draw from this study is that this QBCP model is a favorable situation for the occurrence of spontaneous spin Hall instabilities. No particularly strong or exotic interaction is needed, and the ratio $U'/U \le 1$ between interorbital and intraorbital interactions should not be too unrealistic. The main difficulty regarding possible realizations of these phases is the dispersion with the QBCP. We will come back to this in the conclusions.

Note that the $d$-wave-like wave-vector dependence of the components of the free Hamiltonian and its off-diagonal content that lead to a wave-vector-variation of the Bloch eigenvectors are essential for obtaining these interesting instabilities. If we had just taken a Hamilton matrix $ \mathbf{H}^0(\mathbf{k}) \propto  \mathbf{k}^2 \sigma_z$ that leads to the same dispersion but constant Bloch eigenvectors, the dominant instabilities would have been Stoner ferromagnetism at small $U'/U$ and orbital ordering at larger $U'/U$. These states are neither SN nor support topologically protected edge states.

\section{QBCP on a Checkerboard Lattice}
For possible realizations of the unconventional particle-hole instabilities found in the preceding section, it would further be advantageous to have a lattice model that shows similar physics.
In this section we want to analyze a QBCP on a checkerboard lattice, which has two sublattices $A$ and $B$ playing the role of the orbital degree of freedom in the last section. This model was already studied by Sun \textit{et al.} in mean-field theory for spinless fermions \cite{sun}. Here, we treat the spinful case with the fRG.
 The free Hamiltonian is still of the form of Eqs. (\ref{hfree}) and (\ref{h0}) but with the new hopping terms
\begin{align}
d_I&=2 t_I(\cos k_x + \cos k_y )-\mu \, ,\notag\\
d_x&=8 t_x \cos \frac{k_x}{2} \cos \frac{k_y}{2} \, ,\notag\\
d_z&=2 t_z (\cos k_x -\cos k_y) \, .  \label{latham}
\end{align}
Here, the lattice constant has been set to unity.  $t_x$ corresponds to hopping between nearest neighbors and $t_I$ and $t_z$ correspond to hopping between next nearest neighbors, that is nearest neighbors on the same sublattice. If we again set $t_I=0$, then the hoppings between next nearest neighbors connected by a line in Fig. \ref{lattice} and not connected by a line have opposite sign. We also set $t_x=t_z=t$ and $\mu=0$ as in the last section.

This lattice model has a QBCP around the corner of the Brillouin zone $(\pi,\pi)$ and in its vicinity the lattice model assumes the form of the continuum model in the last section. The dispersion is shown in the right panel of Fig. \ref{lattice}. Further away from the band crossing, the dispersion breaks rotational symmetry around $(\pi,\pi)$.

We consider an onsite repulsion $U$ and a spin-independent nearest-neighbor repulsion, thus, the interaction part of the Hamiltonian reads as
\begin{eqnarray}
H_{\text{int}}\hspace{-0.3cm}&&= \frac{U}{2 N}\hspace{-0.1cm} \sum_{\mathbf{k},\mathbf{k'},\mathbf{q} \atop o,s \ne s'} \medspace \psi^\dagger_{o,s}(\mathbf{k}) \psi^\dagger_{o,s'}(\mathbf{k'})\psi_{o,s'}(\mathbf{k'}-\mathbf{q})\psi_{o,s}(\mathbf{k}+\mathbf{q})\notag\\
&&+\frac{U'}{4 N}  \sum_{\mathbf{k} , \mathbf{k'} , \mathbf{q}  \atop o \ne o',s,s'} \medspace \left(\cos \frac{q_x+q_y}{2} + \cos\ \frac{q_x-q_y}{2} \right) \notag \\ && \times \quad\psi^\dagger_{o,s}(\mathbf{k}) \psi^\dagger_{o',s'}(\mathbf{k'})\psi_{o',s'}(\mathbf{k'}-\mathbf{q})\psi_{o,s}(\mathbf{k}+\mathbf{q}) \, ,
\end{eqnarray}
where we included an additional factor $1/4$ in the second term to compensate that each lattice site has 4 neighboring sites, so that the results are directly comparable to the continuum model.

We carry out a similar fRG-analysis as described in Sec. \ref{continuum model}. Again, for small $U'/U$  we encounter a SN phase which has the same order parameter as in the continuum model given by Eq. (\ref{mfnematic}).
The mean fields of the QAH and QSH phases suggested by the fRG, however, have an additional prefactor due to the local separation of the orbitals and can be written as

\begin{align}
\label{mfqahlattice}
\Phi_{\text{QAH}}&= \sum_{\mathbf{k}} {\Big \langle} \Psi^{\dagger}(\mathbf{k})(I \otimes \sigma_y)\Psi(\mathbf{k}) \Big(-2 \sin \frac{k_x}{2} \sin \frac{k_y}{2} \Big ) {\Big\rangle} \notag\\
&=\frac{1}{2}\sum_{j,\delta,s}\langle \medspace i \medspace D_{\delta}[\psi^{\dagger}_{B,s}(j+\delta) \psi_{A,s}(j) \notag\\&-\psi^{\dagger}_{A,s}(j) \psi_{B,s}(j+\delta)]\rangle \, ,
\end{align}

\begin{align}
\label{mfqshlattice}
\vec{\Phi}_{\text{QSH}}&= \sum_{\mathbf{k}} {\Big\langle} \Psi^{\dagger}(\mathbf{k})(\vec{\tau} \otimes \sigma_y)\Psi(\mathbf{k}) \Big(-2 \sin \frac{k_x}{2} \sin \frac{k_y}{2} \Big){\Big \rangle}\notag\\
&=\frac{1}{2}\sum_{j,\delta,s,s'}\langle \vec{\tau}_{s,s'} \medspace i \medspace D_{\delta}[\psi^{\dagger}_{B,s}(j+\delta) \psi_{A,s'}(j)\notag\\&-\psi^{\dagger}_{A,s}(j) \psi_{B,s'}(j+\delta)]\rangle \, ,
\end{align}

with $j$ denoting the lattice sites of sublattice $A$, $\delta=\pm \frac{x}{2} \pm \frac{y}{2}$, $D_{\pm( \frac{x}{2} + \frac{y}{2})}=1$ and $D_{\pm( \frac{x}{2} - \frac{y}{2})}=-1$. Note that the topological nontrivial phases do not violate local charge conservation despite their unusual appearance. It can be shown that the expectation value of the fermion number operator at a given coordinate remains constant. The current pattern in the QAH state is indicated by the arrows shown in Fig. \ref{lattice}. In the QSH state we get the same pattern for one spin component, but here the current for the other spin component is reversed.

The phase diagram of the lattice model is shown in Fig. \ref{pd-lattice}. It is similar to the one of the continuum model, both phase transitions occur at similar $U'/U$-ratio. As expected the difference between the two models, which lies only in the high energy modes, do not play an essential role for the determination of the leading instability. The low energy instability of a model with a QBCP at the Fermi level can be reasonably well approximated by the continuum model and is presumably quite independent of details of the band structure in the high energy sector.

\begin{figure}
\begin{center}
\includegraphics[scale=0.45]{lattice.eps}
\hspace{0.2cm}
\includegraphics[scale=0.3]{latticedisp.eps}
\end{center}
\caption{Left: Sketch of the Checkerboard lattice with two sublattices A and B indicated by the two different colors. The arrows indicate the current pattern in the QAH and QSH phase. In the QSH phase the current for opposite spins is reversed.
 Right: Dispersion of the lattice Hamiltonian of Eq. (\ref{latham}). }
\label{lattice}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[scale=0.5]{pdlatticeu6.eps}
\end{center}
\caption{Phase diagram of the lattice model as a function of the interorbital interaction parameter $U'$, in units of the intraorbital repulsion $U=6t$. $\Lambda_c$ denotes the critical scale, defined as the scale at which the couplings exceeds four times the bandwidth, obtained with a fRG calculation using $N=48$ patches per band.}
\label{pd-lattice}
\end{figure}

\section{Flows at non-vanishing chemical potential}
\label{sc}

We now want to investigate the instabilities of the QBCP at a finite value of the chemical potential so that the QBCP is shifted away from the Fermi surface. We mainly consider the continuum model of Sec. \ref{continuum model}. However we checked that the results remain qualitatively similar in the checkerboard lattice of the last section, though.

The natural choice for the patching-points of the discretization scheme is to set them on the circular Fermi surface that opens upon changing the chemical potential away from zero, as we are interested in the effective model at low energy. We choose the patching points of the other band without Fermi surface to be at the same positions in momentum space. Again we also used a momentum discretization with additional radial patches.

In all three regimes, we find a critical chemical potential $\mu_{\textrm{crit}}$, above which the leading instability is superconducting. This means that the leading divergence is now for momentum combinations that have total incoming momentum, $\mathbf{k}_1+\mathbf{k}_2=0$ (assuming that the QBCP is at the origin in momentum space).
Typical phase diagrams are shown in Fig. \ref{pdsc}. We see that the critical scale drops for larger $\mu$.

\begin{figure}
\begin{center}
\includegraphics[scale=0.5]{pdmu44.eps}
\includegraphics[scale=0.5]{pdmu60.eps}
\end{center}
\caption{Phase diagram of the continuum model as a function of the chemical potential $\mu$ at $U'/U=0.55$ (upper plot) and $U'/U=0.75$ (lower plot)}
\label{pdsc}
\end{figure}

A further interesting result is, that in the regime, where we get the QAH for $\mu=0$, there is always an intermediate phase, either SN or QSH type, before the superconducting channel becomes strongest. The leading instability of the intermediate phase is determined by the ratio of $U'$ and $U$: above $U'/U=0.6$, it is QSH and below it is SN.

We also addressed the question as to which type of pairing symmetry can be associated to the superconducting instability. It turns out that this question can not be conclusively answered within our approach. Depending on numerical details, in particular, the discretization scheme (i.e., use of one or more radial patches), we obtain two different results, which are most plausible according to our data and which both have an orbital dependence of the order parameter.  In the first case, the pairing has an interorbital $s$-wave-like component and a $d$-wave-like intraorbital component. The second, nearly degenerate, possibility is an odd-parity, i.e., triplet pairing, symmetry that is $p$-wave-like in all orbital combinations, which has relative phase shifts between the orbital components.
From our data, it seems that different superconducting channels are competing, so that numerical details decide which one is leading. As the model studied here has so far not been realized experimentally, we refrain from  a classification of the pairings in this two-orbital situation and from elaborating this situation with refined numerics further. However, a general conclusion from this study is that, upon doping, the interaction-driven instabilities in such QBCP systems generically give way to unconventional superconducting phases.

\section{Conclusion}
In summary, we have investigated the weak coupling instabilities of the QBCP in a two-dimensional fermionic spin-$1/2$ system with an angle-resolved fRG calculation. Comparing the leading instability for different ratios of intraorbital and interorbital interactions, we obtained similar results for the continuum model and the model on a checkerboard lattice. For weak interorbital interaction, the system is unstable toward a spin-nematic (SN) phase. For intermediate $U'$, we encounter the time-reversal-symmetry breaking QAH phase, and for a strong interorbital repulsion, the leading tendency is toward the topological nontrivial QSH phase.
Upon moving the chemical potential away from the band crossing point, the exotic instabilities are replaced by unconventional pairing instabilities at lower critical scale.

Our results with the QBCP at the chemical potential confirm the conclusion from the mean-field analysis by Sun \textit{et al.} \cite{sun}, mainly obtained for the spinless case. They show that the dominant weak-coupling instabilities of a many-fermion system are not only determined by the shape of the dispersion, but that also the wave-vector-dependent orbital composition of the bands has a decisive impact on the preferred ordering tendency.  This holds as well for linear band crossing points, also known as Dirac points. Here, however, the density of states vanishes at the Fermi level, and nonzero, possibly too large interactions strengths are required to find instabilities.

Further research should address where quadratic and other band crossing points can be found in realistic band structures near the Fermi level in order to investigate their potential instabilities. Bilayer graphene is known to provide two QBCPs at the $K$ and $K'$ points of the Brillouin zone \cite{castroneto}, at least if trigonal warping is ignored. The different spontaneous  quantum Hall states in $N$-layer graphene systems have been classified recently in Ref. \cite{zhangjung}, irrespective of what interactions might be necessary to stabilize these states.  Naively, we suspect however that the bilayer case of two QBCPs with short-range interactions will be dominated by instabilities with the wave-vector connecting the degeneracy points, leading to density wave states, as found in a related approach recently by Vafek \cite{vafek2010}.  Interestingly, for a screened Coulomb interaction with dominant scattering with small wave-vector transfer within the neighborhood of given band crossing point, SN and QAH instabilities were also reported for the bilayer situation \cite{vafek2010,vafekyang2010}. Also, mean-field+fluctuations studies of the bilayer model with long-range Coulomb interaction support the possibility of QAH and QSH states \cite{levitov}. Our study with a single band crossing connects well to these finding and shows that if the two crossing point regions are not at all connected by scattering, even QSH instabilities are possible. Future work should map out the full phase diagram of the bilayer system depending on the screening and also trigonal warping.

This work was supported by the DFG research unit FOR 1162. We thank J. Ortloff, S. Raghu, O. Vafek and S.C. Zhang for discussions.

\bibliographystyle{plaindin}

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text:
Otrod
Susan Ward
Portada del libro de Susan Ward
Título del libro:
Betascript Publishing (2010-08-17 )
apto para el cupón
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Notas y citas / Texto breve:
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Susan Ward (born April 15, 1976) is an American actress and model. Ward was born in Monroe, Louisiana. She attended a private,Christian elementary school (Monroe Christian School), in Monroe,LA. She briefly attended Northeast Louisiana University (now University of Louisiana at Monroe) She began modeling at the age of 13, leaving school and moving to New York to do so, deciding to try her hand at acting several years later. After a few years of small TV jobs on All My Children and NBC's short-lived Malibu Shores, she landed her first main role as the heroine on Aaron Spelling's daytime soap opera Sunset Beach, where she played the virginal Meg Cummings.
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Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
Actress, Model (person), David C. Robinson