text:
Volume 12 - Dream of the Moon's Dawn
Chapter 1286 - The Truth Behind the Wedding
"Two years after my father brought my mother back, they got married in Floating Cloud City. Even though my father never knew my mother's true history, he had never felt any complications or reservations towards her because of this."
"In the third year they were together, they had me. In the fourth year, they had Yuanba. In the seventh year… my mother suddenly recovered both her profound strength and her memories over the course of one night."
"After that, she left, leaving behind my father, leaving behind Yuanba and I as well. She had left with a heartless determination, completely severing the destined bond of marriage between herself and my father. She also did not take anything with her. She instead wanted my father, wanted us to forget about her forever, and to never ever go looking for her…"
Even when she said these words now, Yun Che could still sense Xia Qingyue's deep sorrow. He gave a soft sigh before speaking, "Qingyue, she was not being callous or heartless when she did those things. It was because she had no choice but to leave. Otherwise, the moment her aura was discovered, it would only bring down a huge calamity on all of your heads."
The woman who was his one true love, the woman whom he had grandly announced to the entire universe was going to be his future god empress, had become someone else's wife and had even given birth to two children with that man due to her amnesia… There was no man who could maintain his composure when faced with such a result. The more he loved Yue Wugou, the more crazed he would become—to say nothing of the fact that he was the Moon God Emperor as well.
Being found by him would almost certainly result in him killing Xia Hongyi, and even Xia Qingyue and Xia Yuanba as well.
Thus, she had no choice but to leave and she would never be able to return either.
"I know," Xia Qingyue said in a melancholic voice. "But other than that, there were also her feelings towards my foster father… and her guilt."
Yun Che, "..."
"My mother told me that the seven years that she spent together with my father was a period that she felt very safe and happy. My father loved her and she truly did love my father as well. Those years, she had never once thought of getting those lost memories back, in fact she was even afraid… Afraid that her reawakened memories would shatter her current peace and happiness. But… the moment she recovered all of her memories, everything was turned upside down."
"..." Yun Che was only quietly listening but even he felt a heavy stifling sensation settle on him.
The Moon God Emperor had loved Yue Wugou. He had not taken any more concubines because of her, he had built the God Empress Palace for her, he had given her the name "Yue Wugou", had planned to make her his Moon God Empress, had grandly announced her to the entire universe, had completely fractured any and all relationships he had with the Star God Realm over her…
Xia Hongyi had also deeply loved Yue Wugou. The seven years that Yue Wugou had lost her strength and memories were seven years where she was at her weakest and most powerless. During that period of time, it was Xia Hongyi who was by her side through it all, and she had even married Xia Hongyi and had two children with him…
Yue Wugou was undoubtedly a fortunate soul to have met two men who loved her with all of their souls in her life… But the moment the fog over her memories had been lifted, this all turned into heart-rending cruelty.
She had to make a choice.
Choosing Xia Hongyi would cause her to wrong Yue Wuya now and forever, and it would also bring down an enormous calamity on the heads of Xia Hongyi and her two children.
Choosing to leave Xia Hongyi would mean that she would never be able to see her husband and children ever again…
It was indeed a most cruel decision.
Furthermore, she knew she no longer had the qualifications to choose Yue Wuya ever again, the only things she was left with in regards to him were her guilt and her shame.
"After she had chosen to leave us all those years ago, my mother actually did not return to the God Realm. Rather, she… was looking for a quiet and secluded place, a place to die. Because, she felt that her own existence would only bring calamity to my family. And in regards to foster father… She felt too ashamed to ever meet him again."
She had clearly done nothing wrong, yet she had somehow become the biggest sinner… Yun Che let out a deep sigh of sadness in his heart.
"But, in the end, she gave up on ending her own life and returned to the Moon God Realm. Because she wanted to see my foster father one last time, or perhaps she felt that… it was best if she could die by my foster father's own hands."
"But even if she did not kill herself and foster father did not kill her, in actuality, she did not have much time left."
Yun Che was mildly shocked at those words, "You're saying that your mother, she's…"
Xia Qingyue sofly closed her eyes in order to not let Yun Che see the deep pain in them, "Ever since she was severely wounded all those years ago and lost all her profound strength, her vitality was actually being whittled away every year. Those seven years during which she gave birth to Yuanba and I also caused to lose nearly all of the Stainless divine aura she had left in her body. In fact, when she had finally regained her profound strength and memories all of the sudden, it was actually akin to… the final brilliant flourish of a dying sun."
"..." Yun Che was struck completely dumb by those words, he could find no words to say in response to that.
Xia Qingyue's mother had always had a weak constitution and this was something that the entire Floating Cloud City probably knew about. All those years ago, Xia Hongyi had mentioned this and he had also mentioned that her body was extremely weak, and when her condition was serious, even walking would be difficult for her. She had even had a difficult birth when she was giving birth to Xia Qingyue and when Xia Qingyue was born, her entire body was icy cold and her aura was extremely weak. If not for Xiao Ying using all his strength to save her, perhaps she would have lost her life during that birth.
Moreover, it was also for this reason that Xia Qingyue had been betrothed to "Xiao Che" from the moment she was born.
Coupled with that last event, the reason that Xia Hongyi gave to the public regarding the departure of Yue Wugou was that she had passed away from a weak constitution and a serious illness… This was something that nobody ever had any cause to doubt.
"My mother had originally quietly returned to the Moon God Realm, but for some odd reason, she ended up being discovered by other people. This added fuel to the fire and caused my foster father's reputation to suffer great damage. My mother had originally thought that Foster Father would hate and resent her, or perhaps kill her himself, but…"
She softly drew in a breath before continuing, "He told my mother, 'stainless and boundless' was a vow he had made that would last a lifetime, and it was not because she had possessed the Stainless Divine Body nor was it because she had become 'impure'. To him, for her to be able to return again was the greatest blessing that the heavens had bestowed upon him."
"Those weren't just hollow and empty words." Xia Qingyue continued in a soft voice, "After my mother returned to the Moon God Realm, everyone, including the people of the Moon God Realm itself, had expected her to be locked away in some lightless place suffering under foster father's wrath, or maybe she would even be tortured to death… But in truth, over the past few years, she had her own little world and many maidservants who were there specifically to take care of her and meet her every need. Furthermore, foster father went to meet her and accompany her almost every day, and every so often, he would use his own power to extend her life. He also did not hesitate to use the best medicinal pellets in the Moon God Realm on my mother's body."
"If not for all of this, my mother would have departed this world long ago, and I also would definitely not have been able to see her again."
Yun Che was deeply shaken by those words.
It was also at this moment that his impression of the Moon God Emperor completely changed.
The "Yue Wugou" affair that had happened all those years ago had caused the Moon God Emperor to suffer such great humiliation that even Yun Che, who had not been in the Eastern Divine Region for very long, had known about it. In fact, this scandal could even have been termed as the greatest scandal in the history of the Moon God Realm.
No matter how enduring a man was, no one could easily bear such a humiliation, much less the emperor of a king realm. For him to vent all of his anger and resentment on Yue Wugou was something that was actually completely reasonable and natural in the eyes of the world… Even if these people clearly knew that it was not Yue Wugou's fault.
Yet, the Moon God Emperor… had treated the returned Yue Wugou just as he had in the beginning.
Yun Che searched his own heart and he asked himself if he could do as the Moon God Emperor did if he was in his shoes…
"After my mother left, my father felt sick many times during the next year and he would often quietly weep. He would also sit down for an entire day while staring at my mother's portrait… So, I swore when I was a young girl, that I would track down my mother one day so as to prevent my father's tears from flooding his face, and so that my family could finally be reunited again…. And the reason I poured my heart into the profound way was so that I could achieve this very goal."
"Finally, I found my mother in the Moon God Realm, but I also had no choice but to face foster father as well. I once blamed, detested, resented and even hated him. It was all because of him that my father and mother had no choice but to part, it was because of him that my family would never be reunited again… But after that, I slowly heard everything from my mother, and I personally witnessed the unstinting care he showed my mother, so I couldn't continue hating him any longer."
"It was to the point that acknowledging him as 'foster father' was something that I did wholeheartedly."
The Moon God Emperor had saved her life, saved Yu Wugou's life, and had used his own dignity to allow Yue Wugou to truly live a 'stainless' life. So how could she hate him and what could she even hate in the first place?
"The Moon God Emperor… Eh, I mean your foster father, does he know about the Profound Sky Continent and Uncle Xia?" Yun Che probed.
"He does not know," Xia Qingyue said. "My mother was not willing to talk about it, so after foster father asked one time, he did not ask again."
They would never ever let the Moon God Emperor know about Xia Hongyi and when she returned to the Profound Sky Continent in the future, she would never mention the Moon God Emperor to her father either… Perhaps, letting Xia Hongyi forever live with his yearning for Yue Wugou would truly be the least cruel conclusion.
"Then your mother… is she still well?" Yun Che asked again.
"..." Xia Qingyue gave a small shake of her head but she did not reply.
Yun Che felt a faint pain stab into his heart. When she had suddenly regained her profound powers and memories all those years ago, it was already the last flashing brilliance of a dying sun. It had been an entire twenty years since that had happened… If not for the incomparably vast resources of the Moon God Realm and the Moon God Emperor's unstinting generosity towards her, if it was in any other place, it was likely that Yue Wugou would not have been able to persist up to this point.
But it seems like Yue Wugou's lifeforce had just about completely withered away, and even the Moon God Emperor himself was powerless to reverse the situation.
Yue Wuya, the realm king of the Moon God Realm, one of the four god emperors of the Eastern Divine Region, a man who stood at the pinnacle of the Primal Chaos Realm. To think that he would actually have loved a woman with such obsessiveness, through such sorrow… and even to such a humbling extent.
In the end, a god emperor was still a man who shed blood, sweat and tears.
"Then, this wedding celebration, could it be that it… was the fulfill the final long-cherished wish of your mother?"
"...The one who would have completed the wedding ceremony in the end would not have been me, it would have been my mother…" Yun Che now finally comprehended the words that Xia Qingyue had said.
She had given Xia Hongyi seven years and a son and a daughter, but she wanted to give the last bit of her life to Yue Wuya…
So he did not expect Xia Qingyue to shake her head instead.
"Do you know why foster father would intentionally allow me to show my face right before the wedding ceremony?" Xia Qingyue asked.
Those words left Yun Che slightly flummoxed.
No matter whether it was the God Realm or the lower realm, no matter what kind of wedding ceremony it was, the bride would always cover her face, whether it was using a great red veil or a curtain of jade pearls. Furthermore, it was only when they finally entered their bridal chambers that the bridegroom would take this covering off.
At least, for the three wedding ceremonies he had been a part of, besides the time when the Little Demon Empress had married him into her household, the other two times were like that.
(Caizhi: ???)
But Xia Qingyue had shown her face to the crowd before the wedding ceremony had even begun.
At that time, the Moon God Emperor had been agitated by the Star God Emperor's words so he had gotten Xia Qingyue to come out and show herself to all who were present… Now that he thought about it, it seemed as if… it was done so deliberately.
"It was deliberate?" Yun Che asked.
"Yes. It was in order to allow everyone present to remember my aura, especially my aura of Glazed Glass. Furthermore, that should have been the one and only time I showed my face. After the wedding ceremony began, I would have used the 'Moon Star Substitution' art to temporarily project my aura to my mother's body and allow it to cover her. After that, my mother and my foster father would complete the wedding ceremony."
When the Moon God Emperor had personally gone to the Vanishing Moon Celestial Palace to remind Xia Qingyue to complete her "preparations", it was to tell her to prepare to use ''Moon Star Substitution".
Yun Che's heart was beyond moved by these words. Even if the Moon God Emperor himself was more than willing, he was unable to publicly marry Yue Wugou again… because he was still the realm king of the Moon God Realm.
He could only helplessly use this underhanded trick to finally fulfill Yue Wugou's last wish… and perhaps, this was also his greatest wish as well.
At the same time, because Xia Qingyue had the "Heart of Glazed Glass", she could cleanse away the humiliation the Moon God Emperor had felt all those years ago and he could also grandly announce to the universe that the Moon God Realm would receive the protection of the very heavens themselves from this day forth.
The humiliation the Moon God Emperor had suffered all those years ago was due to Yue Wugou, and as Yue Wugou's daughter, Xia Qingyue was undoubtedly entirely willing to help out.
But if this was the case, then why did she shake her head just now? And why did she say just now that this wedding ceremony was not just for the rest of the world to see but it was even more intended for the Moon God Realm itself?
"At the same time, I could also cleanse away the humiliation foster father had suffered all those years ago because of my 'Heart of Glazed Glass', while allowing my mother to find release from the greatest burden in her heart." Xia Qingyue soft words mirrored Yun Che's thoughts, but what she said next caused him to become extremely shocked, "But all of this was not what the wedding ceremony was entirely about."
"The other important goal was to allow me to… to rightfully and properly… succeed the the Moon God Emperor."


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The title of the film above must be familiar to film fans in general and who like to play games. Tomb Raider is a popular series thanks to its game series. Although including a series that is quite old (because it was popular in 2003), since the reboot of the game that was started in 2013 by a well-known Japanese company, Square Enix, the Tomb Raider series became famous again. Square Enix is most commonly known through its game series, Final Fantasy. So that characteristic can be seen in the game Tomb Raider (2013) from the character Lara Croft who increasingly looks realistic.
A little story about the game version, the ancient Tomb Raider series is identical to the figure of Lara Croft, the main character of the series, who looks sexy, and the image is getting stronger after the film starring Angelina Jolie. But since the reboot game in 2013 with the same title (Tomb Raider), Lara's image has …
Best Films Of The Decade
As I used to be pushing aside beginning this high 10 list—an task I always drag my feet on, even though as I write it I invariably pick up steam—I wasted a while making a cup of tea and asking myself what it is about making end-of-year lists that brings up such internal resistance in me. Part of it has to do with the impossibility of quantifying an expertise that, like filmgoing, is by its nature unquantifiable, a paradox that's often decried within the season of awards-giving and record-compiling. So, what are the best movies of all time? The record contains a wide range of films, from artwork home European cinema to prime motion movies and blockbusters to established, extremely-regarded classics of the Golden Age of Hollywood. The entries span many genres and embrace a few of the best film villains created by the very best writers and high film administrators within the industry. Included are films that were acknowledged …
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It's another Wok Wednesday, and an extra special one at that because we've surpassed 800 members! Cue the band! Clang the woks! When I embarked on this journey over two years ago I never could have imagined it would become what it is today – I was just hoping to find others who enjoyed stir-frying as much as I did. Thank you to all who participate!
This recipe is a version of one of my favorite dishes – Singapore Noodles. The version in Stir-Frying to the Sky's Edge comes from Mei IBach, a Chinese Malaysian born in Malaysia and raised in Singapore. When the Chinese came to Malaysia and Singapore they created a fusion cuisine that came to be known as Nyonya – thus, Nyonya-Style Singapore Noodles. You'll see the combination of Chinese and Southeast Asian ingredients in this recipe, which calls for both kecap manis (a Southeast Asian style dark soy sauce) as well as traditional soy sauce.
What did you think about this week's recipe? If you're a fan of Singapore Noodles, how did this version compare to what you usually have? Leave us a comment below and/or a link to your blog post.
This week's recipe stars one of my all-time favorite Asian ingredients – lemongrass. With its slight lemon flavor and floral aroma, lemongrass is widely used across southeast Asia. This recipe combines classical Vietnamese ingredients with time-honored Chinese techniques for one delicious dish!
What did you think of this week's recipe? Leave your thoughts and/or a link to your blog post below.


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\section{Introduction}
Recently two dimensional semiconducting transition metal dichalcogenides (TMDs) of the form MX$_2$, where M = Mo, W, and X = S, Se, have attracted enormous interest because of the possibility of manipulating the valley degree of freedom in addition to spin and charge~\cite{Xiao:2012,Xu:2014,Hao:2016,Mak:2014,Mak:2016,Yang:2015,Kormanyos:2014,Mak2010,Splendiani,Cao:2012}, making them highly promising for low-power electronics and several valleytronics applications. The valley degrees of freedom refer to local extrema in the band structures of these materials, a feature unique to the class of these materials. The valley degree of freedom may also be manipulated as a qubit which opens up new arenas to explore quantum computation with TMDs~\cite{Kormanyos:2014}.
Further, the in-plane mirror symmetry is broken and results in an unusual intrinsic spin-orbit coupling (SOC), called the Ising SOC~\cite{Cappelluti:2013,Zahid:2013,Zhu:2011,Kormanyos:2013}, which originates from the $d$-orbitals of the transition metal. Ising SOC aligns the electron spins near opposite valleys to opposite out of plane directions, thus behaving like a valley contrasting out of plane Zeeman field. Such a spin-orbit field can be sharply contrasted to the Rashba SOC~\cite{Rashba:1959} which aligns the electron spins along the in-plane direction and produces a helical liquid. As a consequence of Ising SOC the valley bands in TMDs are spin-locked even though overall time-reversal symmetry is preserved. This distinctive feature has spurred theoretical and experimental studies in semiconducting TMDs as well as their superconducting counterparts~\cite{Jonker2,Jonker3,Jonker4,Cappelluti:2013,Hao:2016,Kormanyos:2013,Lee:2016,Mak:2014,Mak:2016,Wu:2013,XXu3,XXu4,Xiao:2012,Xu:2014,Yang:2015,Zahid:2013,Zhu:2011, Sharma1,Sharma2,Splendiani,Cao:2012,Kormanyos:2014,Mak2010,XXu1,XXu2,Jonker5}. Moreover the broken spatial inversion symmetry also generates a large Berry curvature near the valleys giving rise to unconventional electronic and optical properties~\cite{Niu:2006}, which have been recently studied in the context of TMDs~\cite{Xiao:2012,Yu:2015,Zhou:2017,Mak:2014}.

In TMDs, due to spin-valley locking the electron spin remains a good quantum number. However, spin may not be conserved if the out of plane mirror symmetry is broken, which can result from a number of processes such as external gating or strain, that are typically present in realistic experimental situations. A Bychkov-Rashba spin orbit coupling~\cite{Bychkov} can thereby naturally arise in TMDs~\cite{Ochoa:2013,Kormanyos:2014} which aligns the electron spins away from the out-of plane direction. The non-trivial role of Rashba SOC has been extensively studied in several materials such as 2D semiconductors~\cite{Bychkov}, quantum dots~\cite{Tsitsishvili:2004}, more recently in  producing topological superconductivity~\cite{Lutchyn}. Despite the fact that Rashba SOC exists in gated TMDs, its role in TMDs has received only limited attention~\cite{Yuan:2014,Kli:2013,Yao:2017,Taguchi:2017}. Very recently the role of Rashba SOC in generating strong Berry curvature effects and anomalous Hall effect has been studied~\cite{Zhou:2017}.

The Nernst effect has been used as a very important experimental probe in a number of physical systems such as high-temperature cuprate superconductors~\cite{AZXu:2000}, charge density waves~\cite{Bel:2003}, and more recently as a probe of strong Berry curvature in Weyl and Dirac semimetals~\cite{Liang:2017}. In conventional Fermi liquids, the Nernst effect is expected to be small due to Sondheimer's cancellation~\cite{Sondheimer}. However, the Sondheimer's cancellation breakdowns for Berry mediated Nernst effect~\cite{Sharma3}, giving rise to a measurable anomalous Nernst current even in the absence of magnetic field. The generation of a Nernst signal in TMDs has been investigated where the intrinsic Ising SOC and Berry curvature effects can generate a pure spin and valley Nernst current~\cite{Yu:2015}.

In this work we show that extrinsic Rashba SOC and intrinsic Ising SOC in gated TMDs can jointly amplify the Nernst signal, which is highly tunable in nature by external gating. The generated Nernst signal is shown to enhance by at least 1-2 orders of magnitude compared to the Nernst signal generated from a purely intrinsic Ising SOC.
We first calculate the Berry curvature due to Rashba SOC, and show that the Berry curvature is strongly enhanced and sharply peaked in the momentum space around the valley points, resembling a Dirac-delta distribution. We then calculate the Nernst response and show that even in the absence of Rashba SOC the Nernst signal at a valley point is shown to be purely dominated by the anomalous geometrical contribution, and the conventional $B-$dependent Nernst signal is significantly weaker for typical material parameters.
The tunable anomalous valley Nernst signal in the presence of Rashba coupling is shown increase by at least one order of magnitude compared to the Nernst signal generated from a purely intrinsic Ising SOC. Although the total Nernst signal, i.e. summing the contributions from both valleys, vanishes due to preservation of time reversal (TR) symmetry, a small external $B-$field lifts the valley degeneracy and further amplifies the Nernst signal by almost two orders of magnitude.

The Nernst effect in bilayer TMDs also has received limited attention so far. Additionally, here we briefly discuss the band structure, Berry curvature of bilayer TMDs~\cite{Kormanyos:2018}, and theoretically examine the generated Nernst signal due to large Berry curvature in these materials. Particularly, we calculate the Nernst response of a 3R and 2H stacked bilayer MoS$_2$. Including the intrinsic SOC effects, the 3R stacked bilayer MoS$_2$ breaks inversion symmetry, unlike the 2H stacked bilayer which remains spin-degenerate. A finite Rashba SOC can enhance and tune the valley Berry curvature of a 3R stacked bilayer. On the other hand a small Rashba SOC generates (and can also tune) a giant Berry curvature in a 2H stacked bilayer due to lifting of spin-degeneracy. We calculate the anomalous Nernst response and show that Rashba SOC can also enhance and tune the Nernst signal in bilayer TMDs.
Our predictions can be directly tested in experiments, and can be employed for several promising caloritronics applications.

This paper is organized as follows: in Section II we discuss the Hamiltonian and the Berry curvature of monolayer TMDs in the presence of Rashba spin orbit coupling, and show the tunability of the Berry curvature with the Rasba parameter. In Section III we discuss the Nernst effect in monolayer TMDs, showing the enhancement and modulation of the anomalous Nernst coefficient with Rashba SOC. In Section IV, we discuss the band structure, Berry curvature and Nernst effect in bilayer TMDs focusing on 3R stacked bilayer MoS$_2$ and 2H stacked bilayer MoS$_2$. We then also discuss the enhancement and tunability of the anomalous Nernst coefficient in both these cases.
Finally we summarize and conclude in Section V.

\begin{figure}
	\includegraphics[scale=0.21]{Mos2_o3_o4_vs_alphaR.pdf}
	\includegraphics[scale=0.21]{Mos2_o1_o2_vs_alphaR.pdf}
	\includegraphics[scale=0.11]{BCmesh_tmd1_alpha_0.jpg}
	\includegraphics[scale=0.11]{BCmesh_tmd1_alpha_4.jpg}
	\caption{(color online) Tunable Berry curvature in TMDs. \textit{Top Left:} The Berry curvature of the conduction bands can be tuned by varying $\alpha_R$. \textit{Top Right:} The valence bands do not show significant variation with $\alpha_R$ becasue $\alpha_R\ll l_v$.  \textit{Bottom Left:} Berry curvature near the valley point for $\alpha_R=0$. \textit{Bottom Right:} Berry curvature near the valley point for $\alpha_R=4meV$ displaying a higher magnitude and a much a sharper peak at the valley point $\mathbf{K}$. The parameters here are chosen for MoS$_2$.}
	\label{Fig_Berry_curv1}
\end{figure}

\section{Hamiltonian and Berry curvature}
We begin with the low energy $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian for a generic monolayer TMD, which is given by~\cite{Xiao:2012}
\begin{align}
H_0 = at (\tau k_x \sigma_x+ k_y\sigma_y) + \frac{\Delta}{2}\sigma_z
\end{align}
where $a$ is the lattice constant, $t$ is the effective hopping integral, $\Delta$ is the bare energy bandgap, $\mathbf{k}$ is the momentum measured from the valley point $\mathbf{K}$, and $\sigma_i's$ represent Pauli matrices for the electron bands. The intrinsic spin orbit coupling can be represented by the following Hamiltonian~\cite{Xiao:2012}
\begin{align}
H_{SO} = \lambda_c \tau \frac{\sigma_0+\sigma_z}{2} s_z + \lambda_v\tau\frac{\sigma_0 - \sigma_z}{2} s_z
\end{align}
where $\lambda_c$ ($\lambda_v$) is the intrinsic Ising spin-orbit coupling in the conduction (valence) band, $s_i^s$ represent Pauli matrices for the electron spin, and $\tau\in\{+1,-1\}$ is the binary valley index. This intrinsic SOC lifts the spin-degeneracy and the bands become spin-polarized.
In addition to the intrinsic spin orbit coupling, a Bychkov-Rashba coupling can also arise in TMDs broken out-of-plane mirror symmetry due to external gating. In the context of the $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian this term can be written as~\cite{Ochoa:2013}
\begin{align}
H_R = \alpha_R (\tau \sigma_x s_y - \sigma_y s_x)
\end{align}
where $\alpha_R$ is the strength of the Bychkov-Rashba SOC. The total Hamiltonian is thus given by
\begin{align}
H = H_0 + H_{SO} + H_R
\label{Eq_H_tot}
\end{align}
The energy eigenvalues of the Hamiltonian $H$ specifically at the valley points (i.e. $\mathbf{k}=0$) are
\begin{align}
&E_{n\tau} = n \frac{\lambda_c \tau}{2} - n\frac{\lambda_v \tau}{2} \nonumber \\
&\pm \frac{1}{2} \sqrt{(\lambda_c + \lambda_v)^2 + \Delta^2 + 2n\Delta\tau (\lambda_c+\lambda_v) + 8\alpha_R^2 (1-n\tau)}
\end{align}
where $n\in\{+1,-1\}$.
The spin degeneracy in the conduction bands is broken as a result of $\lambda_c$ and $\alpha_R$. Unlike $\lambda_c$ which is an intrinsic SOC, the Rashba SOC allows us to tune the energy bands by external electrostatic gating.

The presence of Berry curvature in TMDs can result in anomalous transport responses such as the anomalous Hall, spin Hall and the Nernst effects~\cite{Niu:2006}.
The Berry curvature for a generic $m^{th}$ band is given by the expression
\begin{align}
\Omega_{ab}^m = i\sum\limits_{m\neq m'}\frac{\langle m|\partial H/\partial k_a|m'\rangle \langle m'|\partial H/\partial k_b|m\rangle -(a\leftrightarrow b )}{(E_m' - E_m)^2} \nonumber \\
\label{Eq_Berry_curv}
\end{align}
The presence of a finite Rashba SOC can thus allow us to manipulate the Berry curvature of the electron bands. Even though the Berry curvature for the Hamiltonian $H$ in Eq.~\ref{Eq_H_tot} can be evaluated analytically, the exact expressions are cumbersome and we do not provide them here. Instead, we directly numerically calculate the Berry curvature and related quantities.
Fig.~\ref{Fig_Berry_curv1} shows the calculated Berry curvatures of the conduction bands as a result of tuning the Rashba SOC parameter $\alpha_R$. We note that the Berry curvature of the conduction bands can increase up to atleast 1 order of magnitude greater than the valence bands for typical values of $\alpha_R$. On the other hand, the valence band Berry curvature stays close to the orbital (intrinsic) Berry curvature ($\Omega_{\mathbf{K}} = -2a^2t^2 / (\Delta-\lambda_v)^2$) as the intrinsic SOC $\lambda_v \gg \alpha_R$ typically for all TMDs. The spin splitting $\lambda_c\sim\alpha_R$ and the Berry curvature in conduction bands is strongly affected by both parameters, $\lambda_v$ and $\alpha_R$. Interestingly, we also note that Rashba SOC not only enhances the Berry curvature contribution for the conduction band but also sharpens the peak at the valley point as demonstrated in Fig.~\ref{Fig_Berry_curv1}. The intrinsic Berry curvature scales as $\sim 1/(1+k^2)$ around $\mathbf{K}$ but the Rashba mediated Berry curvature has a much sharper distribution, closely resembling a Dirac-delta function. This is expected because the Chern number of the band is a topological invariant, and therefore a sharp peak in the Berry curvature must be compensated by reducing contributions from  the neighboring points in momentum space.

\section{Nernst effect in monolayer TMDs}
 Nernst effect refers to the generation of a transverse electric field in the presence of a longitudinal temperature gradient. Conventionally, the Nernst effect should occur only in the presence of an external magnetic field, which provides a transverse velocity to the electrons by the Lorentz force. However, a non-trivial Berry curvature $\mathbf{\Omega}_\mathbf{k}$ of the bands can also give rise to a Nernst response as a result of an anomalous velocity term~\cite{Niu:2006} genrated by $\mathbf{\Omega}_\mathbf{k}$.
A non-zero Nernst response is expected only when overall time-reversal symmetry is violated. In doped TMDs the contribution from the spin-up and spin-down bands exactly cancels out each other as the system preserves time-reversal symmetry.
The anomalous Nernst coefficient is given by the product of the anomalous velocity and the entropy density~\cite{Tewari:2008}
\begin{align}
\alpha_{xy} = \frac{k_Be}{\hbar} \sum\limits_{m=1}^{4}{\int d^2\mathbf{k } \Omega^m_{\mathbf{k}} s^m_{\mathbf{k}}}
\label{Eq_alphaxy_anom}
\end{align}
where $m$ is the band index, $s_{\mathbf{k}} = -n_f \log n_f - (1-n_f) \log (1-n_f)$ is the entropy density, $n_f$ being the Fermi distribution function. It is important to point out that the anomalous Hall conductivity $\sigma_{xy}$ directly depends on the Berry curvature of the filled bands, but on the other hand $\alpha_{xy}$ is a Fermi surface quantity, because $s_{\mathbf{k}}$ is zero for completely filled and completely empty bands.
\begin{figure}
\includegraphics[scale=0.21]{alphaxy_vs_mu_various_tmds_1.pdf}
\includegraphics[scale=0.21]{alphaxy_vs_mu_tmd1_variousT_1.pdf}
\includegraphics[scale=0.21]{anom_alphaxy_twoTMDs_100K.pdf}
\includegraphics[scale=0.21]{std_alphaxy_twoTMDs_100K_3T.pdf}
\caption{(color online) \textit{Top Left:} Anomalous Nernst coefficient (in the units $k_B e/\hbar$) at the valley $\tau=1$ as a function of chemical potential $\mu$ for various TMDs at $T=50K$. \textit{Top Right:} Anomalous Nernst coefficient (in the units $k_B e/\hbar K$) at valley $\tau=1$ for MoS$_2$ at various temperatures. The Rashba SOC parameter was chosen to be $\alpha_R = 0$. \textit{Bottom left:} Anomalous Nernst coefficient (units $SnVK^{-1}$) at $\tau=1$, $\alpha_R=0$ and $T=100K$. \textit{Bottom right:} Conventional $B-$dependent Nernst coefficient (units $SnVK^{-1}$) at $\tau=1$ at $T=100K$ and $B = 3T$. The contrast in the magnitudes can be noted.}
\label{Fig_alphaxy_1}
\end{figure}
\begin{figure}
	\includegraphics[scale=0.33]{Nernst_tmd2_vs_mu_1.pdf}
	\includegraphics[scale=0.18]{density_tmd2_1.jpg}
	\caption{(color online) \textit{Top:} Anomalous Nernst coefficient (in the units $k_B e/\hbar$) at valley $\tau=+1$ as a function of the chemical potential $\mu$ calculated for WS$_2$. For $\alpha_R>0$ the Nernst coefficient shows a significantly enhanced signal compared (by at least one order of magnitude) to the Nernst coefficient contribution from only intrinsic SOC. \textit{Bottom:} Density plot for the anomalous Nernst coefficient for various values of $\alpha_R$ and $\mu$. The sharp peaks when $\mu$ is tuned to partially fill up one of the conduction bands is a striking feature which emerges from a finite Rashba SOC. }
	\label{Fig_alphaxy_2}
\end{figure}
It is for this reason, that an insulator can give rise to an anomalous Hall response ($\sigma_{xy}$), but not an anomalous Nernst response $\alpha_{xy}$.
Typically in Fermi liquids the conventional Nernst effect is expected to be small due to Sondheimer's cancellation~\cite{Sondheimer}, which breakdowns of for Berry mediated Nernst effects, as shown recently~\cite{Sharma3}.

\begin{figure}
	\includegraphics[scale=0.1]{BCmesh_sumoftwovalleys_tmd1_B_15T_alpha0.jpg}
	\includegraphics[scale=0.1]{BCmesh_sumoftwovalleys_tmd1_B_1T_alpha4.jpg}
	\includegraphics[scale=0.17]{density_BC_tmd1.jpg}
	\caption{(color online) \textit{Top Left:} The magnitude of the sum of Berry curvatures (in units $\AA^2$) in the two valleys for a particular conduction band in MoS$_2$ when $B=15T$ and $\alpha_R=0$. For $B=0$ we do not expect a net Berry curvature due to TR symmetry. \textit{Top Right:} Same as the left plot but for $\alpha_R=4meV$ and $B=1T$. The Berry curvature now shows a much sharper peak around $\mathbf{K}$ which is more than one order of magnitude greater the former case even for a very small $B$ field.  \textit{Bottom:} Density plot of the sum of peak Berry curvature for various $B$ and $\alpha_R$ values.}
	\label{Fig_Berry_2}
\end{figure}
\begin{figure}
	\includegraphics[scale=0.36]{Total_alphaxyanom_tmd1_difB_alpha4.pdf}
	\includegraphics[scale=0.36]{Total_alphaxyanom_vsB_tmd1_difmu_alpha4.pdf}
	\caption{(color online) Total (summing contributions from both valleys) anomalous Nernst coefficient calculated for MoS$_2$. A small $B$-field breaks TR symmetry and the valley symmetry resulting in a large net Nernst response when the chemical potential is tuned appropriately. We chose $T=50K$ and $\alpha_R=4meV$. A large net Nernst signal as a result of a small $B$-field is a distincitive feature in these materials even though the $B-$field by itself is not expected to produce such a large Nernst signal.}
	\label{Fig_totalNernst}
\end{figure}
The anomalous Nernst coefficient is calculated from Eq.~\ref{Eq_alphaxy_anom} by integrating the Berry curvature up to the chemical potential. In Fig.~\ref{Fig_alphaxy_1} we plot the anomalous Nernst coefficient for various TMDs for $\alpha_R =0$. The anomalous Nernst coefficient picks up a non-zero signal for partially filled conduction bands and its magnitude is proportional to the Berry curvature of the respective bands. In the presence of a finite magnetic field TMDs also will exhibit a conventional Nernst response which is given by~\cite{Ziman}
\begin{align}
\alpha_{xy} = \frac{e^3 \tau_s^2 B}{T\hbar} \int{d^2\mathbf{k} (E - \mu)\left(-\frac{\partial n_f}{\partial E}\right) \left(\frac{ v_x^2\partial^2 E}{\partial^2 k_y^2} - \frac{v_xv_y \partial^2E}{\partial k_x\partial k_y}\right)}
\end{align}
where $\tau_s$ is the scattering time and $v_i$ is the semiclassical velocity. In order to compare the magnitude of the anomalous part of the Nernst coefficient in TMDs with the conventional one we also calculate the latter within the relaxation time approximation, which is valid in the limit $\omega_c\tau_s\ll 1$, $\omega_c$ being the cyclotron frequency. For typical values~\cite{Brumme} of $\tau_s$ and relevant $B-$ fields we find that this condition is satisfied. Fig.~\ref{Fig_alphaxy_1} shows a comparison of the anomalous and conventional Nernst coefficients. Even when $\alpha_R=0$ the Berry curvature mediated Nernst response is at least 3 orders of magnitude bigger than the conventional Nernst coefficient.

In Fig.~\ref{Fig_alphaxy_2} we plot the anomalous Nernst coefficient at valley $\tau=+1$ as a function of the chemical potential $\mu$ calculated for WS$_2$. For $\alpha_R>0$ the Nernst coefficient shows a significantly enhanced signal compared (by at least one order of magnitude) to the Nernst coefficient contribution arising just from intrinsic SOC ($\alpha_R=0$). The figure also shows the density plot for the anomalous Nernst coefficient for various values of $\alpha_R$ and $\mu$. The sharp peaks in the Nernst signal when $\mu$ is tuned to partially fill up one of the conduction bands is a striking feature which emerges in these systems from a finite Rashba SOC. As the chemical potential is varied from the bottom of the lower conduction band to the upper conduction band, the Nernst signal changes sign because the sign of the Berry curvature is opposite in the two neighboring bands.

Our discussion so far was focused on the Nernst coefficient contribution from a single valley in TMDs. We noted that the anomalous Nernst contribution is significantly larger than the conventional Nernst coefficient. Further the anomalous contribution can be enhanced by at least one order in magnitude as a result of tuning the Rashba SOC $\alpha_R$, but the conventional Nernst isn't much altered with a finite $\alpha_R$. However, as a result of preservation of TR symmetry the Berry curvature satisfies $\Omega^m_{\mathbf{K}} = -\Omega^m_{-\mathbf{K}}$, and thus the total (summing contributions from both valleys) Berry curvature, and hence the total Nernst coefficient exactly vanishes. Nevertheless, breaking the valley degeneracy can result in a finite flux of the Berry curvature and therefore a finite total Nernst effect. One way to generate such asymmetry is by applying a small external magnetic field perpendicular to the 2D plane. The magnetic field acts on the valley and spin sectors as $H^s_z = b_z s_z$, and $H^v_z = \sum\limits_a m^a b_z$, where $b_z$ is the magnetic field, $s_z$ is the spin-Pauli matrix, and valley orbital magnetic moments $m^a$. The orbital magnetic moment is given by
\begin{align}
m^a = \frac{ie}{2\hbar} \sum\limits_{a\neq a'}\frac{\langle a|\partial H/\partial k_x|a'\rangle \langle a'|\partial H/\partial k_y|a\rangle +c.c}{E_a - E_a'} \nonumber \\
\label{Eq_Berry_orb}
\end{align}

The terms $H_z^s$ and $H^v_z$ can then be added to the total Hamiltonian in Eq.~\ref{Eq_H_tot}. The role of external magnetic field is to break time reversal symmetry and lift the band degeneracy between $+\mathbf{K}$ and $-\mathbf{K}$. As a result the system now possesses an net flux of the Berry curvature. A conventional Nernst coefficient will also be generated in the process of applying an external $B-$field, however it is of a much smaller magnitude compared with the anomalous contributions.
In Fig.~\ref{Fig_Berry_2} we plot the magnitude of the sum of Berry curvatures in the two valleys for a particular conduction band in MoS$_2$ for a finite magnetic field. When $B=0$ we expect a vanishing net Berry curvature everywhere.
We note that for $\alpha_R=0$, we need a large $B-$field in order to generate even a small net Berry curvature. However a small finite $B-$field in conjunction with a finite $\alpha_R$ produces a large net Berry curvature (at least 2 orders of magnitude larger) with a very sharp distribution (resembling a Dirac-delta distribution) around the valley point $\mathbf{K}$, clearly distinct from the $\sim 1/(1+k^2)$ distribution for intrinsic Berry curvature.

In Fig.~\ref{Fig_totalNernst} we plot the total Nernst coefficient for MoS$_2$ in the presence of a finite magnetic field. In plotting this we integrated the Berry curvature of both valleys up to the chemical potential.
The sharply peaked net Berry curvature distribution around the $\mathbf{K}$ point and a finite Rashba SOC produce an amplified anomalous Nernst coefficient, which can be easily tuned by external gating. It is important to emphasize the role of an external magnetic field, which by itself cannot produce the Nernst signal of this magnitude but is crucial in generating Berry curvature asymmetry between the two valleys. Interestingly, similar behavior for the Nernst response has been recently proposed~\cite{Sharma3} and observed~\cite{Liang:2017} in Dirac semimetals. Even though Dirac semimetals are rather quite distinct from TMDs, the close similarity in their Nernst response is an universal manifestation of underlying non-trivial band topology.

\section{Nernst effect in bilayer TMDs}
So far our discussion was focused on Nernst response in monolayer TMDs. The Nernst response in bilayer TMDs has received limited attention so far. The anomalous Nernst effect in bilayer TMDs is directly related to its Berry curvature properties, which in bilayer TMDs has both inter-layer and intra-layer contributions~\cite{Kormanyos:2018}. Further, the stacking of monolayers also effects the band spectrum and the Berry curvature in bilayer TMDs~\cite{Kormanyos:2018}. Like monolayer TMDs, bilayer TMDs also exhibit a finite Berry curvature, which leads to anomalous transport and optical properties, such as the valley and spin Hall effects. As a prototype, we will discuss (i) 3R stacked bilayer MoS$_2$, and (ii) 2H-stacked bilayer MoS$_2$. As we will examine, both of these materials can exhibit a large Nernst effect of purely anomalous origin, tunable with Rashba spin orbit coupling. Since, we already showed in the previous section that the conventional ($B-$ field dependent) contribution to the Nernst signal is small compared to the anomalous contribution, we will neglect this conventional contribution in our analysis and just focus on the anomalous contribution.

\subsection{3R stacked bilayer}
We first discuss 3R stacked bilayer MoS$_2$, which break inversion symmetry~\cite{Kormanyos:2018}. Due to inversion symmetry breaking Berry curvature is expected to play an important role in transport properties. Near the $\mathbf{K}$ points, the low energy Hamiltonian up to the lowest order in $k$ can be written as
\begin{align}
H^{3R}=\left( \begin{array}{cccc}
\epsilon_{cb}^b & \gamma_3 k^+ & \gamma_{cc} k^- & 0 \\
\gamma_3 k^- &   \epsilon_{cb}^v   & 0 & \gamma_{vv} k^- \\
\gamma_{cc} k^+ & 0 & \epsilon_{cb}^t   & \gamma_3 k^+\\
0 &\gamma_{vv} k^+  & \gamma_3 k^- &  \epsilon_{vb}^t
\end{array} \right)
\label{Eq_H_3R}
\end{align}
where the momentum $k^{\pm} = (\tau k_x \pm i k_y)$ is measured from the valley points. The subscripts $vb$ and $cb$ refer to valence and conduction bands respectively, while $t$ and $b$ refer to the top and bottom layer respectively. $\gamma_3$ is the intra-layer coupling between the conduction and the valence band (similar to $at$ in the monolayer case), while $\gamma_{cc}$ and $\gamma_{vv}$ are the inter-layer couplings between top and the bottom layers. From Eq.~\ref{Eq_H_3R} it is clear that the Berry curvature will have both intra-layer ($\gamma_3$ dependent) contributions, and inter-layer ($\gamma_{cc}$ and $\gamma_{vv}$ dependent) contributions. For example, at the $\mathbf{K}$ points, the Berry curvature for the conduction band is given by
\begin{align}
\Omega_{\mathbf{K}} = \frac{1}{2} \left(\frac{2\gamma_3}{\epsilon_{cb}^b - \epsilon_{vb}^b}\right)^2 \pm \frac{1}{2(\epsilon_{cb}^b-\epsilon_{cb}^v)^2} \gamma_{cc}^2
\end{align}
for the top/bottom later, and similarly one may derive an expression of the Berry curvature for the valence band. For typical material parameters, we find that the contributions of inter-layer and intra-layer on the Berry curvature are of comparable order of magnitude. The above Hamiltonian does not  contain the spin-orbit coupling effects, which may be accounted for by adding the terms $\Delta_{cb} s_z \tau_z$ and $\Delta_{vb} s_z \tau_z$ to the conduction and the valence bands respectively, where the Pauli matrices $s_z$ and $\tau_z$ act on spin and valley space. Note that $\Delta_{vb}\gg \Delta_{cb}$, as is the case in monolayer TMDs. Spin-orbit coupling splits the spin-degenerate bands in both the conduction and the valence bands, though its effect on the conduction bands is rather small.

\begin{figure}
	\includegraphics[scale=.33]{Berry_3R_tmd_bilayer_vs_rashba.pdf}
	\includegraphics[scale=.2]{density_totnernst_5T_blayer_3R.jpg}
	\caption{\textit{Top panel:} Berry curvature (in units $\AA^2$) of four out of the eight bands of a 3R stacked bilayer MoS$_2$. The Berry curvature is easily tunable with Rashba spin orbit coupling and can be enhanced up to two orders of magnitude for typical $\alpha_R$ values. \textit{Bottom panel:} The total anomalous Nernst coefficient for a magnetic field of $5T$, tunable with the chemical potential and $\alpha_R$. }
	\label{Fig_bilayer_1}
\end{figure}
\begin{figure}
	\includegraphics[scale=.215]{E_2H_bilayer_r0.pdf}
	\includegraphics[scale=.215]{E_2H_bilayer_r8.pdf}
	\includegraphics[scale=.215]{2H_bc5_bc6_vs_r.pdf}
	\includegraphics[scale=.115]{2H_alphaxyanom_density.jpg}
	\caption{\textit{Top panel:} Conduction band spectrum of 2H stacked bilayer MoS$_2$ for $\alpha_R=0$ (left) and $\alpha_R=8meV$ (right). The band degeneracy is lifted by a finite Rashba soc. \textit{Bottom panel:} The conduction band Berry curvature (left) at the $\mathbf{K}$ point as a function of $\alpha_R$, which displays a giant peak for small finite $\alpha_R$. Anomalous valley Nernst coefficient (right) $\alpha_{xy}$ as a function of $\mu$ and $\alpha_R$. }
	\label{Fig_2H_bilayer_1}
\end{figure}
\begin{figure}
	\includegraphics[scale=.215]{2H_bilayer_E_r_36mev.pdf}
	\includegraphics[scale=.215]{2H_Bilayer_Berry_r32to38.pdf}
	\includegraphics[scale=.21]{2H_tot_nernst_1T.jpg}
	\caption{\textit{Top panel:} Conduction energy bands (left) and the Berry curvature in the units of $\AA^2$ (right) for 2H stacked bilayer TMD at large values of Rashba SOC. At certain value of $\alpha_R$, two of the bands cross each other leading to a peak in the Berry curvature along with a sign change. \textit{Bottom panel:} Total anomalous Nernst coefficient ($\alpha_{xy}$) of a 2H stacked bilayer MoS$_2$ for a magnetic field of $B=1T$.}
	\label{Fig_2H_bilayer_2}
\end{figure}

Let us now discuss the tunability of the Berry curvature in the presence of Rashba spin orbit coupling. Fig.~\ref{Fig_bilayer_1} shows the peak Berry curvature at the $\mathbf{K}$ point as a function of the Rashba spin orbit coupling parameter ($\alpha_R$) for four of the total eight bands of a 3R stacked bilayer MoS$_2$. The Berry curvature is easily tunable with Rashba spin orbit coupling and can be enhanced up to two orders of magnitude for typical $\alpha_R$ values. Similar to the case of a monolayer TMD, we can expect a large anomalous valley Nernst signal, which is easily tunable via Rashba spin-orbit coupling. Again, due to preservation of a TR symmetry, the net Nernst signal must vanish. A small perturbative magnetic field, can however break valley symmetry. The magnetic field acts on the valley and spin sectors i.e. $H^s_z = b_z s_z$, and $H^v_z = \sum\limits_i m^i b_z$, for magnetic field $b_z$ and valley orbital magnetic moments $m^i$. Although, the magnetic field has a small effect on the band-structures of these materials, its role in generating a valley asymmetry and thus a large overall Berry curvature is crucial. Fig.~\ref{Fig_bilayer_1} shows the total anomalous Nernst coefficient for a magnetic field of $5T$, which is tunable with the chemical potential and $\alpha_R$, showing sharp peaks at certain values of chemical potential.

\subsection{2H stacked bilayer}
The low energy $\mathbf{k}\cdot \mathbf{p}$ Hamiltonian for 2H stacked bilayer MoS$_2$ is given by
\begin{align}
H^{2H}=\left( \begin{array}{cccc}
\epsilon_{cb} & \gamma_3 k^+ & \gamma_{cc} k^- & 0 \\
\gamma_3 k^- &   \epsilon_{vb}   & 0 & t_{\perp} \\
\gamma_{cc} k^+ & 0 & \epsilon_{cb}   & \gamma_3 k^-\\
0 &t_{\perp}  & \gamma_3 k^+ &  \epsilon_{vb}
\end{array} \right)
\label{Eq_H_2H}
\end{align}
where $t_{\perp}$ is the tunneling between the holes of top and bottom layer. Unlike 3R stacked bilayer, the above Hamiltonian is inversion symmetric. Therefore the Berry curvature vanishes identically everywhere. The spin-orbit coupling effects can be accounted for by  $\Delta_{cb} s_z \tau_z \sigma_z$ and $\Delta_{vb} s_z \tau_z \sigma_z$ to the conduction and the valence bands respectively. However, even in the presence of SOC, the energy bands in 2H stacked bilayer remain degenerate (see Fig.~\ref{Fig_2H_bilayer_1}), leading to vanishing Berry curvature. A finite Berry curvature can be generated via: (i) a finite inter-layer potential $U_g$ which breaks symmetry between the top and the bottom layers, or (ii) gate-tunable Rashba spin-orbit coupling. The effect of inter-layer coupling has been explored in Ref.~\onlinecite{Kormanyos:2018}, and we will not discuss that here. Here we will explore the effect of Rashba spin-orbit coupling on the band-structure, Berry curvature and the Nernst effect in 2H stacked bilayer TMDs.

The evolution of band spectrum due to Rashba SOC is shown in Fig.~\ref{Fig_2H_bilayer_1}. Even in the presence of intrinsic SOC (but absence of Rashba SOC), the 2H bilayer spectrum is spin-degenerate, with vanishing  Berry curvature near a valley point. A finite Rashba SOC lifts the spin degeneracy  at and away from the $\mathbf{K}$ point. We note that due to an infinitesimal Rashba SOC, the band degeneracy is lifted and a giant peak in the Berry curvature is generated. This behavior can be contrasted to the smooth Berry curvature enhancement in 3R stacked bilayer MoS$_2$ (see Fig.~\ref{Fig_bilayer_1}) when $\alpha_R$ is increased from zero. Consequently, an anomalous valley Nernst coefficient, tunable with Rashba SOC, is generated (also shown in Fig.~\ref{Fig_2H_bilayer_1}), displaying peaks when the chemical potential touches the energy bands. Another interesting behavior occurs for large values of Rashba SOC. When the Rashba SOC parameter is increased further, at a certain critical $\alpha_R$ the bands cross each other (see Fig.~\ref{Fig_2H_bilayer_2}). This band crossing also generates a peak in the Berry curvature along with a distinct sign change (Fig.~\ref{Fig_2H_bilayer_2}). Thus, even though the 2H stacked bilayer by itself does not display peculiar Berry curvature effects, a small finite Rashba coupling can lead to striking modulation of the Berry curvature.
Now, we can apply a small magnetic field which breaks the valley symmetry, and thereby generates a large overall anomalous Nernst effect. Fig.~\ref{Fig_2H_bilayer_2} shows the total anomalous Nernst coefficient ($\alpha_{xy}$) of a 2H stacked bilayer MoS$_2$ for a magnetic field of $B=1T$, tunable with Rashba SOC.

\section{Conclusion}
 In this work we analyzed the Nernst response of monolayer and bilayer TMDs. The Nernst response typically has two electronic contributions - the conventional $B-$field dependent contribution, where the anomalous velocity to the electrons is provided by the Lorentz force, and secondly the the anomalous  contribution where the anomalous velocity is provided by the Berry curvature.
 We first showed that the Nernst signal at a valley point in TMDs is purely dominated by the anomalous geometrical contribution and the conventional $B-$dependent Nernst signal is significantly weaker for typical material parameters.
 Further, we showed that the interplay of gate controlled Rashba SOC and intrinsic Ising SOC in gated monolayer TMDs can produce a large valley Nernst signal of purely geometrical origin in monolayer TMDs, which is highly tunable in nature.
The tunable anomalous valley Nernst signal in the presence of Rashba coupling can be enhanced by at least one order of magnitude. Although the total Nernst signal vanishes due to preservation of TR symmetry, a small magnetic coupling can lift the valley degeneracy, and an amplified net Nernst signal of almost two orders of magnitude larger can be achieved.

Additionally, we also analyzed the band structure, Berry curvature, and Nernst effect in bilayer TMDs, focusing on 3R and 2H stacked bilayer MoS$_2$ as a prototype. Including just the intrinsic SOC effects, the 3R stacked bilayer MoS$_2$ breaks inversion symmetry, unlike the 2H stacked bilayer which remains spin-degenerate. We showed that a finite Rashba SOC can enhance and tune the valley Berry curvature of a 3R stacked bilayer. On the other hand a small but finite Rashba SOC generates (and can also modulate) a giant Berry curvature in a 2H stacked bilayer due to lifting of spin-degeneracy. When the Rashba SOC is increased further, then at a certain critical $\alpha_R$ the bands cross each other and another peak in the Berry curvature is generated along with a distinct sign change. Consequently, we also showed that Rashba SOC can enhance and tune the anomalous Nernst effect in bilayer TMDs.
Our predictions can be directly tested in experiments, and may be employed for several promising tunable caloritronics applications.

redpajama_set_name: RedPajamaArXiv


text:
Nation Current Affairs 13 Oct 2017 If my car is not saf ...
If my car is not safe, what about 'aam aadmi': Kejriwal writes to Lt Guv
Published Oct 13, 2017, 9:49 pm IST
Updated Oct 13, 2017, 9:49 pm IST
Arvind Kejriwal's blue Wagon-R, which he used till the 2015 Assembly election and in many ways helped cement his 'aam aadmi' image, was stolen from outside the Delhi Secretariat on Thursday. (Photo: PTI)
New Delhi: Delhi Chief Minister Arvind Kejriwal on Friday shot off a letter to Lt Governor Anil Baijal, saying the theft of his car points towards the rapidly "deteriorating" law and order situation in the national capital.
Kejriwal also wondered what the people of Delhi should expect when the chief minister's car gets stolen from outside the secretariat, which is the headquarters of the local administration.
"My Wagon-R car was stolen outside the Delhi Secretariat. My car getting stolen is a small matter. But the fact that it went missing outside the Delhi Secretariat reflects the rapidly deteriorating law and order situation in Delhi," Kejriwal wrote.
Read: No trace of Kejriwal's missing WagonR, AAP announces 'suitable award'
He went on to take a jibe at the Delhi Police saying that upon receiving his letter, the police will try to paint a rosy picture of law and order in the city by sharing favourable statistics.
"What can the common men expect in a state where the chief minister's car goes missing? Delhi's law and order has been rapidly deteriorating over the last few months. Police and law and order comes directly under you. Please make the system robust. We are ready to cooperate," he wrote.
Read: Arvind Kejriwal's Wagon R goes missing from outside Delhi Secretariat
Kejriwal's blue Wagon-R, which he used till the 2015 Assembly election and in many ways helped cement his 'aam aadmi' image, was stolen from outside the Delhi Secretariat on Thursday.
The hatchback was being used by an Aam Aadmi Party (AAP) functionary over the last few months.
Tags: aam aadmi party (aap), delhi secretariat, arvind kejriwal, delhi police, blue wagon r stolen
Location: India, Delhi, New Delhi
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text:
Q: How to filter records by date with laravel? I have a filter like this

I have a working date filter with laravel. The problem is that if I don't filter my records when no records are shown.
public function index(Request $request)
{
    $stats = [
        'done' => UserTransaction::where('status', UserTransaction::STATUS['done'])->count(),
        'canceled' => UserTransaction::where('status', UserTransaction::STATUS['canceled'])->count(),
        'all' => UserTransaction::count(),
    ];
    if ($request->start_date && $request->end_date){
        $dateS = new Carbon($request->start_date);
        $dateE = new Carbon($request->end_date);
        $result = UserTransaction::whereBetween('created_at', [$dateS->format('Y-m-d'), $dateE->format('Y-m-d')])->get();
    }
    if ($request->search) {
        $transactions = UserTransaction::search($request->search)->paginate(5);
    } else {
        $transactions = UserTransaction::paginate(5);
    }
    if ($transactions->count() == 0 && $request->search ) {
        msg()->warning('No records found');
    }
    return view('transaction::admin.index', compact('transactions', 'stats', 'result'));
}

A: You can use if condition inside query and remove outer if condition
$result = UserTransaction::where(function($query)use($request){
    if(!empty($request->start_date)&&!empty($request->end_date)){

      $dateS = new Carbon($request->start_date);
      $dateE = new Carbon($request->end_date);
      $query->whereBetween('created_at', [$dateS->format('Y-m-d'), $dateE->format('Y-m-d')]);
    }
    })->get();

A: I would consider changing your logic a little to allow for people to specify either just a start date or just an end date which could be entirely possible from a usability perspective.
Create a query builder, then add where clauses for the start_date and end_date if they appear in your $request object. If they do not appear then you can use the query as you have been doing so already.
$transactions = Transaction::query();

if ($request->start_date) {
  $query->whereDate('start_date', '>=', new Carbon($request->start_date));
}

if ($request->end_date) {
  $query->whereDate('end_date', '<=', new Carbon($request->end_date));
}

if ($requer->search) {
  $query->search($request->search);
}

$query->paginate(5);

redpajama_set_name: RedPajamaStackExchange


text:
[![BuddyBuild](https://dashboard.buddybuild.com/api/statusImage?appID=59d904ff8588d60001729c4e&branch=master&build=latest)](https://dashboard.buddybuild.com/apps/59d904ff8588d60001729c4e/build/latest?branch=master)

The simplest way to **read** and **respond** to your GitHub notifications on iOS.

## What

GitHawk is a small iOS app that makes managing GitHub accounts and projects a little easier. It exists because GitHub's mobile interface is missing features and is slow.

It is also proof that you can build rather complicated Swift apps with [IGListKit](https://github.com/Instagram/IGListKit).

## Why

- Push `IGListKit` + Swift to its limits
- Enable project management on mobile
- Explore [GitHub's GraphQL API](https://developer.github.com/v4/)
- Scratch my Swift-itch
- Create a real, complex app in the open

## How

GitHawk will be released with (at least) a three-phased rollout:

1. Basic, "read only" version.
    - Read notifications for PRs and Issues
    - React to comments
    - Mark notifications as read
2. Add replies to PRs and Issues
    - Close, lock, and re-open PRs and Issues
    - Label PRs and Issues
3. Repo management
    - Browse & create Issues
    - Browse PRs
    - Create & delete labels
4. Northstar
    - Browse PR content
    - Accept, reject, and merge PRs
    - :rocket:

## Installation

If you want to build GitHawk locally, run `npm install`. It will install [apollo-codegen](https://github.com/apollographql/apollo-codegen) that is required to generate the
GraphQL models.

## Open Source & Copying

I ship GitHawk on the App Store for free and provide its entire source code for free as well. In the spirit of openness, I have licensed my work under MIT so that you can use my code in your app, if you choose.

However, I ask that you **please do not ship this app** under your own account. Paid or free.

## Contributing

:warning: This repo is moving _fast_! :warning:

If you would like to test the latest changes, you can join the TestFlight by sending your e-mail address to [@_ryannystrom](https://twitter.com/_ryannystrom) in a DM on Twitter.

I'm happy to take PRs, but I'm working off of `master` at the moment, and your PR might go stale quick. Be warned!

You'll also need a [Client ID and Client Secret](Setup.md).

Once this is released and development slows down I might get more formal about our work. Until then, its the wild, wild west.

redpajama_set_name: RedPajamaGithub


St. Thomas will enter this weekend's championships as the favorite to win the team title as the Tommies will look to win their 10th consecutive MIAC Indoor Championship. Gustavus, Bethel, and host Concordia will likely pose the biggest threat at stopping St. Thomas' run. While Saint Benedict, Carleton, St. Catherine, and Hamline all have the talent to compete for one of the top spots in the conference. St. Olaf, Macalester, Augsburg, and Saint Mary's will rely on strong individual performances to help them move upward in the team standings.
The Auggie women will be a young team in 2009, with just six juniors and seniors on the roster. The key to success for the Auggies this season will be continued improvement from its eight first-years and a goal of scoring more points at conference for its returners.
Augsburg's top performer in 2008 returns to anchor the Auggies in the sprints. Whitney Holman (JR, New Hope, Minn./Robbinsdale Armstrong HS) finished second in the 55 meters and fifth in the 200 meters at the 2008 MIAC Indoor championships, earning all-conference and honorable-mention all-conference honors. Holman was named MIAC Track Athlete of the Week, for the second time in her career in early February and will look to have a strong season again in 2009.
Also returning for the Auggies will be Gaby Hamerlinck (JR, St. Paul, Minn./Highland Park HS) in the jumps and Sadie Dietrich (SR, Luverne, Minn.) in the middle distances. Hamerlinck is currently ranked top eight in the high jump on the MIAC performance list with a height of 1.52 meters and will be looking to score points for the Auggies at conference. Dietrich was the Auggies No. 2 runner in cross country this fall and will be looking to qualify for conference in the middle distances.
Newcomer Caroline Senungi (FY, Shoreview, Minn./Mounds View HS) will be looking to score points for the Auggies in the hurdles this season. Senungi finished fifth in the 55 meter hurdles in her collegiate debut with a time of 9.06 at the St. Olaf invitational. Kacie Bahr (FY, Brainerd, Minn.) and Kristin Bunge (FY, Preston, Minn./Fillmore Central HS), also newcomers for the Auggies, will be looking to make an impact in the middle distances.
Head Coach Jim Timp believes the 2009 season looks to be a good opportunity to continue with the success that was experienced last year with the women's team finishing in third place at the indoor conference meet - just half a point out of second.
The women's squad is led by four captains: Marie Borner (Sr., Cottage Grove, Minn.), who is the defending national champion in the indoor mile run and has earned an automatic qualifying time in the 800 meter run as well; Vanessa Moore (Sr., Grantsburg, Wis.), who is on her way back to the NCAA Championship meet in the high jump; Heather Jelen (Sr., Sioux Falls, S.D.), who is an All-MIAC and NCAA All-Region cross country runner; and Michaela Otto (Jr., Cottage Grove, Minn.). Huldah Omesa (So., Brooklyn Park, Minn.) has been performing well in recent competitions, and could be a factor in a couple of different events.
The coaching staff is very excited about this year's teams. Depth has been the problem over the past couple of years which has prevented the Royals from being one of the top teams. The talent has been there and now the depth seems to be there as well. With this kind of talent and depth and the leadership and commitment that exist, the squads seems to be poised to move up once again in the MIAC.
Carleton's championship drive at the upcoming MIAC finals will be spearheaded by freshmen Simone Childs-Walker and Clare Franco.
Simone Childs-Walker has established herself as a commanding force in only her first year of collegiate competition. Childs-Walker made her MIAC track debut in convincing fashion, winning both the mile and 3000-meter events at the St. Olaf Triangular, meriting the honor of MIAC Women's Indoor Track Athlete of the Week for January 26. Her performance in that race still stands as the fastest 3000-meter run in the MIAC.
However impressive, Childs-Walker's success has come as little surprise to those who followed the Knights' 2008 cross country campaign. Childs-Walker was the team's top runner and placed third overall in the fall's MIAC cross country championships. She once garnered recognition as MIAC women's cross country athlete of the week, receiving the distinction on October 20.
Other accolades reaped by Childs-Walker include turning in Carleton's second best 5000 meter time and best since 2003, spanning the distance in 17:49.49 on February 6th against St. Benedict. That time is tops in the MIAC this year, by over 18 seconds.
On the 21st of February at the Parent's Day Open she ran the 3000 meter race in 10:01.63, the best time in the conference this year.
Alongside Childs-Walker will be the Knights' other freshman phenom, Clare Franco, who, in her first two collegiate meets, has set school records in the 400 and 600 meter dashes. At the Carleton Women's Dual meet on February 6, Franco covered the 400-meter dash in a blistering 58.73 seconds, missing a provisional qualifying time by only 0.03 seconds. It is also the second fastest time run in the MIAC this year. Her sprint into Carleton's record books also includes running the 600 meter race in 1:38.32.
Carleton's hopes of success in mid-distance races will also hinge on the performances of Laura Roach and Taylor Ffitch. Roach was victorious at the Meet of the Hearts, where she earned the conference's third best 1000 meter time of the year. A week later at the Parent's Day Open, Roach recorded the MIAC's fourth fastest mile time of the season, with a time of 5:09.38.
Taylor Ffitch has collected multiple wins in her stellar rookie campaign. Most notably, Ffitch has prevailed in the mile at the Meet of Hearts with a time of 5:18.60. Ffitch also won the 3000 meter race against St. Benedict with a time of 10:39.42, the third fastest in the MIAC.
Concordia will try and continue their recent trend of top tier finishes at the MIAC Indoor Championship Meet when they host the meet on Mar. 6-7. The Cobbers finished fourth at last year's conference meet but have posted eight top three finishes in the past 11 years and are the only other school other than St. Thomas to win an indoor championship title.
Once again the Cobbers will have a stellar middle distance and distance crew as well as a deep field team. The only national provisional qualifier so far for the Cobbers is multi-event athlete Leah Kay. She posted a provisional score of 3,314 in the pentathlon and is currently fourth in the country. Kay is also ranked eighth in the long jump and third in the high jump where she has also posted a national provisional mark. The other top Cobber in the MIAC so far this season is Alexa Kleingartner. She is ranked first in the 55-meter hurdles in a time of 8.81.
Concordia athletes that are in the top 10 in the conference include Kristina Bruns in the long jump and triple jump. Tatijana Mueller-Dahlberg in the triple jump as well Kristen Warren in the shot put and Emily Davis in the weight throw. Alyssa Deutschmann in the high jump and Tessa Comstock in the pole vault round out the top 10 field athletes. Kristin Slette is in the top 10 in the 400 meters and Hailey Brenden in the 3000 and 5000 meters.
The Gustavus women's indoor track and field team looks to finish near the top of the team standings at the 2009 MIAC Indoor Track and Field Championship title after earning second place at the 2008 Championships.
The Gusties will be led by junior Kaelene Lundstrum (Bird Island, Minn.), the reigning conference champion in the high jump and the pentathlon. One of the top all-around athletes in the MIAC, she is currently ranked in the top five of three events including second in the shot put (42-4 3/4), fourth in the 55-meter hurdles (9.05), and fourth in the high jump at 5-3 1/4.
Gustavus hopes to utilize its depth in the field events to grab several points for the team standings. The Gusties hold three of the top five marks in the league in the shot put as all-conference athlete senior Lisa Brown (Lake Crystal, Minn.) is first at 43-1 followed by Lundstrum in second and sophomore Sam Broderius (Hector, Minn.) in fifth at 39-8 1/2. Two Gusties are also currently seeded in the top five of the weight throw as juniors Anna Bauer (Hastings, Minn.) and Diana Scott (Bristol, Conn.) are second (49-11) and fifth (46-8), respectively. In the long jump, sophomore Janey Helland (Mapleton, Minn.) is currently seeded second with a distance of 16-11 1/2.
Other athletes ranked in the top eight on the MIAC Performance list are returning all-conference pole vaulter junior Meredith Halling (Rochester, Minn.), who is ranked sixth at a height of 10 feet, sophomore Megan Lundgren (Mankato, Minn.), who is sixth in the 600 meters (1:39.96), and junior Becca Bryson (Alden, Minn.) is eighth in the long jump (16-3 3/4).
Gustavus will enter a pair of strong relay teams to the conference meet as the 4x200 relay team of Dani Serbus (So., Franklin, Minn.), Julia Thompson (So., Cannon Falls, Minn.), Sam Frings (Fy., Coleraine, Minn.), and Megan Lundgren is seeded second at 1:50.73, while the 4x400 relay team is seeded fourth at 4:10.27. This group consists of Frings, Abby Karl (So., St. Cloud, Minn.), Janey Helland, and Lundgren.
A talented corps of runners lead the 2009 Piper women into the MIAC indoor championships as they look to improve upon their eighth-place finish from 2008.
Distance runner Margot Branigan (Jr., Roseville, Minn.) and sprinter Kameron Argiannis (So., Eden Prairie, Minn.) have led the Pipers with impressive finishes throughout the winter. Branigan most recently won the 5,000 meter race at the University of Minnesota, besting her next closest competitor by nearly ten seconds with a finish of 18:07.68. In the fall, she qualified for cross country nationals, finishing 53rd.
Joining Branigan in the distance events will be Freya Fitzer (Sr., North Oaks, Minn.), Jessica Kociscak (So., Anoka, Minn.) and Katie Drinane (Sr., Roseville, Minn.), who have been taking successful fall cross country campaigns and turning them into event wins throughout the indoor season.
Argiannis will lead the sprinters after taking over at the top of the Hamline record books in both the 200-meter dash (27.27) and 600-meter dash (1:37.52) following a break-out winter. In just her first-year on the track in 2008, she won the outdoor MIAC 400-meter hurdles championship while running an NCAA provisional time (63.82).
Veteran Nicole Brohmer (Sr., La Crosse, Wis.) and newcomer Katelyn Frenchick (Fy., Paynesville, Minn.) will also look to add points to improve the Pipers' standing in sprint events.
An athlete with diverse talents, Katelyn Anderson (So., White Bear Lake, Minn.), will make an impact for the Pipers both as a sprinter and in the field events. Anderson holds the Hamline school record in the pole vault, and has been impressive in the long and triple jumps, as well as making her presence felt this winter in the 200-meter dash.
Macalester's lineup has been reduced by study abroad commitments from some top performers, but the Scots are looking for some good performances from several individuals.
Sprinter Emily Matthews (Jr., Fort Collins, Colo.) was fourth last winter in the 55-meter dash and is looking to move up into All-MIAC range in Moorhead. Matthews is joined in the sprints by Maddie Mette (Jr., Burnsville, Minn.) and Mari Mejia (So., Golden Valley, Minn. / St. Louis Park). Mette and Mejia will also help out in the jumps.
The Scots are looking for points in the middle and long-distance races from Tara McCoy (So., Menomonie, Wis.), Libby Tollefson (So., Billings, Mont.) and Emma Swinford (Fy., Columbus, Ohio / Grandview Heights).
The College of Saint Benedict Indoor Track and Field Team is geared up for the MIAC Championship held on March sixth and seventh in Moorhead, MN.
After taking fifth in last year's championship, the Blazers look to crack the top four in the conference with an experienced group of athletes. Notable competitors for the Blazers include senior jumper and co-captain Mary Schletty, who set an NCAA Provisional mark and new school record in the triple jump earlier this season with a jump of 11.69 meters, and junior Alyx Chapman, who also set a new school record in the mile with a time of 5:20.05. Other athletes looking to make a mark in the championship include sophomore sprinters Abby Neigebauer and Jillian Daleiden, sophomore mid-distance runner Ashley Irons, junior jumper Ali Galzki and junior thrower Heidi Golliet.
Overall, Saint Benedict has a very balanced squad that can contribute points in many areas. After already competing with tough competition within the conference earlier in the season, the Blazers feel prepared to make a large impact. And with confidence stemming from a young but experienced team, Saint Benedict is prepared to have successful efforts come through at the MIAC Championships.
With a team that has tripled in size since third year coach Mike Henderson took over, the College of St. Catherine track and field team is hoping that a balanced team, with potential point scorers in a variety of event areas, will allow the 2009 Wildcats track and field team to build on the 13 school records they set during the 2008 track season.
The Wildcats will be looking for returning school record holders and MIAC point scorers Sarah Meissner (sprints/hurdles), Greta Sieve (distance), Celest Ventura (throws), Kim and Kayla Engel (Sprints), Amanda Manship (mid-distance) and Sami Larson (throws) to lead a talented group of first year athletes that includes Katie Lawler (sprints), Sam Levercom (sprints) , Sydney Malanaphy (hurdles), Cassie Rooney (jumps), and Heidi Sande (mid-distance) to new heights at the MIAC Championships.
On the women's side, Teri Heinzen (Marshfield, Wis.), Sara Harstad (Chatfield, Minn.) and Brittany Kuehn (Sauk Rapids, Minn.) were the Cardinals' top point scorers a year ago at the conference championships, and from what head coach Shawn McMahon has seen thus far this season, the trio is primed to pick up where they left off.
"The women will rely heavily on Teri, Sara and Brittany as the main point-scorers," said McMahon, noting that Heinzen was seventh in last year's 200 at the indoor conference meet, and has been virtually unstoppable during this year's indoor season, while Kuehn took 10th in the 800 in the same meet. "The experience that Sara picked up as a freshman (last season) should push her into the top of the MIAC in both the shot and the (20-pound) weight."
"We¹ll be looking to our young distance and sprint groups to also capitalize on a lot of race experience from a year ago."
The St. Olaf women's track and field team will compete in the MIAC Indoor Track and Field Championships, held in Moorhead this weekend.
Pole-vaulter, Amie Fillmore, took first in her event in four different meets throughout the season and tied for sixth in the Parents Day Open meet, hosted by the University of Minnesota. Her performances during the Bethel open and the UW-River Fall's Coca Cola Classic earned her provisional qualifications for the NCAA championship meet. After earning her first qualification at the Bethel Open, she was named MIAC's women's field athlete of the week.
Also in the field, triple jumper, Susan Kenzie finished first place as well as sixth in her event in the St. Olaf Invitational and in the Parents Day Open meet respectively.
Sprinters Abby Smith, Callie Knaeble, and Jaime Mosel preformed well throughout the season. Smith won the 800 meter run during two different meets. Knaeble finished third in the 55 meter dash and second in the 200 meter dash in two different races during the Bethel Open. Mosel took a first place in the 400 meter run.
Distance runners Annie Knutson, Jenna Carlson and Katie Duwell, attained respectable achievements. Knutson raced well enough to gain second and third place in the mile and 3000 meter run during the season. She also took second in a 5000 meter run. Duwell took third in one of her 1000 meter races.
Coach Joe Sweeney and his team are looking to capture St. Thomas' 10th consecutive MIAC women's indoor track and field championship at this weekend's 12-team competition in Moorhead.
In the 2008 indoor meet in Collegeville, sophomore Nikki Arola had a hand in five victories to lead St. Thomas to a runaway victory. The Tommies set records for points scored (233) and margin of victory (134.5) as they won 12 events and scored in all 18 events they entered.
Sweeney's Tommies also won the 2008 outdoor track and meet, aided by four Arola victories, and won a narrow team victory at last fall's MIAC cross country meet. The Tommies now have won 61 of a possible 79 conference team titles in CC and track in Sweeney's era, including nine in a row since March 2006.
Arola is a threat from the 55 meters to the 400 and on the sprint relay. The Tommies expect big points from thje 600 to the 3,000 races with senior All-American Katie Theisen, junior All-American Erin Sprangers, junior Kelly Russ, and sophomores Raynee DeGrio and Allie Metzler leading the charge.
On the national Division III charts, St. Thomas is seeded fifth in the distance medley relay and eighth in the 4x400, and Theisen (mile) and Arola (400) have strong NCAA provisional times.
In the MIAC indoor season lists, St. Thomas is seeded first in seven events, seeded second in five events, rank third in three events, and rank fourth in nine events.