# Virtual talk

I’ll be doing my first virtual seminar this week. I was scheduled to visit the Flatiron institute in NYC this week, and obviously that was not going to happen, so I’ll be giving the talk from the comfort of my dining table 🙂

The talk is Tuesday 12pm east coast time, so 9am for me. I’ll be talking about some recent and on-going work in which Oleg Starykh, Anna Keselman and I study how you can observe *interactions* between quasiparticles in quantum magnets from the dynamical structure factor.

https://www.simonsfoundation.org/event/quantum-cafe-leon-balants/

and yes…they quite systematically mis-spelled my name!

# Why come to UCSB?

This is the season in which students are deciding where to go for graduate school in the US. Around the country, students have been admitted to PhD programs, passing through a remarkably selective filter. To give you an idea, we typically get something like 600-700 applicants for what we hope will be 20-30 incoming students in all fields of physics. It’s a tough competition, and those that make it are a talented bunch. After that, the shoe is on the other foot. These students invariably have multiple offers, and now *they* have to choose where to go. The deadline to respond to our offer is generally tax day, April 15 (and as far as I know this is pretty much true everywhere). So we’re getting close.

Normally physics departments invite these “prospective” students to a day-long visit of the campus, to meet professors and students, and learn more about the program. With COVID-19, we like many others canceled the visit, which would have been yesterday, and held instead a virtual visit. I spent 4.5 hours yesterday on Zoom with prospectives. It worked pretty well but I can’t help but wonder what got lost in the mix. For example, we normally hold a poster session with current students showing their work to the prospectives, there are casual events to discuss, etc. It all was pretty compressed and intensified by the last-minute change to virtual space.

So…I thought maybe it would be useful to give a few advertisements for UCSB physics, focusing on condensed matter because well that’s what I know best.

• We’ve got a big and top-notch condensed matter theory effort. Apart from myself, there are five physics faculty working in quantum matter theory: Matthew Fisher, Chetan Nayak, Cenke Xu, Andreas Ludwig, and starting this fall Sagar Vijay. But that’s not all. Microsoft Quantum has several permanent scientists that advise students: Bela Bauer, Roman Lutchyn, Parsa Bonderson. There are a number of computational theorists in other departments: Chris van der Walle, Vojtech Vlcek, Glenn Fredrickson (Glenn does polymer physics, which is classical not quantum, but recently his group has discovered they can use their polymer algorithms to simulate quantum spins or bosons!). We also have a number of theorists in soft and living matter, which isn’t quantum but neverthess we share a lot of ideas in common: Boris Shraiman, Cristina Marchetti (Cristina and I go way back – we collaborated back in the 90s!), Mark Bowick. There’s also some convergence of interest with the string/gravity group, where chaos and scrambling, SYK models, etc. are being actively studied.
• Don’t forget our postdocs! The KITP has a track record of hosting the best postdocs in the world, and it hasn’t changed. They are young, motivated, and brilliant, and they are eager to work with our students. Typically we have about a half dozen overall in condensed matter and quantum information.
• More is different: Probably the most unique feature of UCSB is all the collaborative opportunities.
• In theoretical physics at the center is the KITP: take a look here to see the 16 programs already scheduled for the next 1.5 years. Each one will bring 20-30 world-class scientists *every week* to the KITP to present their research, discuss ideas, and start new collaborations. It’s an amazing opportunity for our students to learn new things and gain valuable exposure.
• There’s Microsoft Quantum, which is next door to the KITP and 5 minutes from the Physics department.
• The new UCSB Quantum Foundry is an NSF sponsored center aimed to develop the quantum materials needed for quantum information science. I am part of “Thrust 1” whose goal is to study highly entangled matter such as spin liquids and topological superconductors. The Foundry offers collaborations, seminars, fellowships and more for students.
• I am the co-director of the international program on Quantum Materials run through CIFAR. It’s a collaborative network of currently 15 scientists (theorists, experimentalists, and sample growers) from around the world interested in the deepest questions in the field. We meet a couple of times a year with students and postdocs and visitors to discuss and chart new research directions.
• UCSB is a member of the Simons Collaboration on Ultra-Quantum Matter, which combines condensed matter, quantum information, atomic, and string theorists to study the nature of highly entangled and quantum critical matter. The Collaboration holds schools and meetings, and encourages exchanges of members.
• We are an EPiQS Theory Center sponsored by the Moore Foundation. This supports some of those great postdocs and beyond.
• That’s not all – I just got tired to typing. There are even more collaborations and multi-university efforts that students can become a part of.
• It all connects to experiment: My personal favorite part of the field is connecting to real-world measurements in the lab. I have a lot of friends at UCSB who make those measurements. Stephen Wilson in materials grows new materials all the time, and we’ve been collaborating constantly on quantum magnets, spin liquids, Mott insulators, and superconductors. Susanne Stemmer is one of the top thin film (MBE) growers in the world, and has made many advances in correlated and topological materials. Andrea Young‘s lab is bursting with new discoveries in 2d materials such as twisted bilayer graphene, which provides a rich source of phenomena for theory to tackle. We keep hiring great young experimentalists in both the physics and materials departments, in both condensed matter and amo physics, and beyond this networks such as CIFAR and EPiQS, MURI grants, and more give students even more access to exciting experiments — and arguably I am pretty good at teaching them how to connect these with theory.
• Our students are successful. The vast majority of the condensed matter theory group’s students stay in academia, and find permanent research positions.

# Benefits of teaching

I taught this August in a summer school in Cargèse, Corsica, which is an island in the Mediterranean that is part of France. It was an especially fun trip for me as I attended a school at the same location in 1993, as a graduate student. Other students there with me were Leo Radzihovsky, Ali Yazdani, Katherine Moler, and Dan Dessau, to name a few that come immediately to mind. They all did rather well in physics since!

Anyway, I decided to lecture about twisted bilayer graphene (TBG), which was a bit of an undertaking – I gave 6 hours of lectures over 4 days. You can find my hand-written lecture notes on this site (under pedagogy), and I’m working on a latex version (I have them for 3 out of four of the 1.5 hour lectures).

I already benefited myself from the class, because it motivated me to finally work out an old idea I had. This is a derivation of the “continuum model” of Bistritzer and MacDonald (BM), which is what really started the whole TBG discovery by predicting the presence of “magic angles”. Their work is really nice, and many others have since used their formulation to elaborate or extend the treatment in many ways. I always felt though that the derivation in BM’s paper was not so intuitive, and the final result – the continuum model – is simpler than the way it was obtained. Specifically it just seems to capture the idea that locally TBG just “looks” like an untwisted bilayer with some relative shift between layers. I had the idea after reading their paper that one could derive the continuum model by turning that idea into a calculation.

There is some subtlety related to the difference between Eulerian and Lagrangian coordinate systems which stymied me initially. But since I had to teach the stuff I was motivated to spend the time and I was able to overcome that issue. The result is so simple it borders on trivial, but I like the simplicity of it. Maybe it makes the problem a bit more accessible to some people. You can read about it here: https://arxiv.org/abs/1909.01545.

# Santa Barbara Astronomical Unit

Yesterday I gave a talk to the Santa Barbara Astronomical Unit – a local group of astronomy enthusiasts who meet at the Santa Barbara Museum of Natural History. I don’t do astronomy or astrophysics but it was a nice group of people curious about physics in general. I told them about Quantum Materials, giving a number of relations to astrophysics.

The group does a lot of outreach and if you want to learn about the sky and how to observe it, and live in the area, check them out at http://sbau.org/.

# Catching up

It’s been too long since I last wrote. One tends to get busy. Quite a bit has happened since April. I went to a rock concert with my daughter for the first time. I lectured on quantum spin liquids at a summer school in Capri (nice place!). I attended a conference in Tbilisi, in the republic of Georgia – an extremely interesting destination full of ancient and modern history – and a GRC in Hong Kong which impressed upon me how far topological materials have come. I also got a glimpse of the protests there, which is inspiring in another way.

A few new initiatives are starting. I’m happy to report we’ve received a renewal of the KITP’s EPiQS grant from the Moore Foundation, to support postdocs in quantum materials theory for the coming 5 years. I’m also part of a new Simons Collaboration on Ultra-Quantum Matter, which starts in September.

Our group has put out a few new papers/preprints. I’ll give something of a quick summary:

• With Oleg Starykh, we posted a paper about the dynamical structure factor of the U(1) quantum spin liquid with a spinon Fermi surface in two dimensions, in an applied magnetic field. It’s the first time I really fully engaged with this challenging problem, described theoretically by fermions coupled to a Landau-damped gauge field, in order to try to really sort out some of its spectral properties. We found surprisingly that there should be a sharp (not infinitely well-defined) collective mode which could be sought experimentally.
• Chunxiao finally posted his encyclopedic paper (with Gábor Halász) on Z2 spin liquids on the pyrochlore lattice and proximate ordered states. This has been years in the making, but taken back seat to other more pressing things. Lots of work there – thanks Chunxiao and Gábor!
• With Urban Seifert, a student of Matthias Vojta from Dresden, who visited here earlier this year, we developed a fully quantum theory of ultra-fast laser excitation of antiferromagnets, with application to Sr2IrO4. I found this a stimulating introduction to non-equilibrium driven dynamics of quantum many body systems, a subject I hope to work much more on in the future.
• I also enjoyed a number of experimental collaborations. I’ve had a few projects with Stephen Wilson, an experimentalist in our materials department at UCSB. We just published a paper on NaYbO2, which is an effective S=1/2 triangular lattice antiferromagnet and a possible quantum spin liquid. I collaborated with Kamran Behnia’s group at ESPCI in Paris, to understand physical properties of and quantum transport through domain walls in Mn3Sn – see the paper. I helped David Hsieh’s group at Caltech understand spin correlations in the paramagnetic regime of the ferromagnetic material CrSiTe2, which they probed by nonlinear optics. Most recently, I worked with Andrea Young’s group to understand aspects of their recent discovery of zero field quantized quantum anomalous Hall effect in twisted bilayer graphene. These experiments are amazing! My Science paper with Lucile Savary, Takehito Suzuki, and Joe Checkelsky has also finally appeared. This took *a long time* to publish mainly because my experimental friends Joe and Takehito were extremely responsible and conscientious about taking time to vet and prove a sample growth recipe that could be shared and readily reproduced. Making quality materials is hard work!

Right now I’m preparing for lectures at a summer school in Cargèse, Corsica, where I’ll be teaching in just under two weeks. I decided to talk about the theory of twisted bilayer graphene, which has been moving so fast it feels rather challenging to cover!

# CIFAR Quantum Materials

Come this summer, I will be taking on a new role: co-director of the Canadian Institute for Advanced Research’s “Quantum Materials” program. This is a program with a 30 year history that began around the discovery of high-Tc superconductivity and managed to make Canada into a powerhouse in that area. Over the years, it evolved into a more international effort, and broadened to embrace what we now call quantum materials (arguably the name originated from the program). I’ve been a regular member for a number of years, and what is impressive about this program has been the way everyone involved comes together to really try to connect materials synthesis, experiment, and theory for greater understanding and impact. I’m not Canadian but I do very much respect the effort and I’ll be joining Louis Taillefer in the re-imagining of this program starting in July. This is not a physical institute, and the main activities are meetings to foster collaborations, and to train students and postdoctoral scientists. I’m excited about the team Louis and I are putting together, and hope we can keep up the traditions and impact of the program going forward.

You can find out more on CIFAR’s web site: https://www.cifar.ca/research/programs/quantum-materials

# Landau fans in TBG

There’s a lot of excitement over twisted bilayer graphene (TBG), and increasingly over other sorts of moiré heterostructures from 2d materials. In TBG, most of the interest is due to the discovery of many correlation phenomena that occur at partial filling of the mini-bands nearest the charge neutrality point. Theory says that they are very flat, and have novel topological aspects to them. The flatness explains their tendency to be unstable to interactions that induce the correlated states. But the details of that flatness still matter to any theory. There are lots of models for this – how do we know what is right? It would be great to be able to actually measure the bands in experiment.

The most sensitive way to measure bands experimentally is via quantum oscillations. Semiclassically, these are oscillations as a function of doping/field/etc due to interference of electron trajectories that go in closed orbits in momentum space. So one can learn about these orbits. Quantum mechanically, this is due to Landau level formation. Anyway, many groups have seen quantum oscillations in TBG in the regime where correlated states form. But guess what? They do not really agree with the naïve explanations based on most band theories. There are many discrepancies, but the most obvious one is that even close to charge neutrality, the “magic angle” samples do not show the oscillations that would be expected from Dirac cones at the corners of the moiré Brillouin zone. The expected behavior is actually seen at larger angles. So something different happens near the magic angles that needs to be explained.

My students Kasra Hejazi and Chunxiao Liu and myself wondered if the differences might be related to topological changes that happen near the magic angles, in the “standard model” of these systems due mainly to Bistritzer and Macdonald. So these guys set out to do a fully honest calculation of the quantum oscillations. This is a variant of the Hofstadter “butterfly” problem, and the true electron spectrum is actually fractal. But they managed to subdue the beast of a challenge and work things out rather completely. Short answer: for certain angles in the “magic range” one indeed gets anomalous quantum oscillations consistent with experiment just from band structure. This is associated with additional topological transitions, or semi-classically to orbits that are not near the moiré zone corners.

This could be an explanation of the experiments! But maybe it is just a piece of the puzzle. The electron-electron interactions can and probably do modify the quantum oscillations. Maybe they could even “fix” the one dis-satisfying feature of our calculations: the anomalous oscillations only occur for a rather narrow range of angles. Maybe interactions make them more robust?

Anyway, the paper is out there – have a look: https://arxiv.org/abs/1903.11563

# On the challenges of reading papers

This post is really just for fun. Everyone knows that reading a professional level paper at the forefront of research is often challenging. This morning I printed out a copy of a paper I wanted to read, from a pdf in my browser. The result was even more difficult to understand than usual:

Quite remarkable! Now it’s not impossible that the author of this paper is reading this. If so, can you identify it? A hint to that person is that I wanted to read it based on a recent visit I made to the author’s university.

# Moiré is better

I’ve taken too long of a hiatus from writing here.  Now seems like a good time to get back on the horse. Here at the KITP we just finished a two week Rapid Response program on “Correlations in Moiré Flat Bands” (follow the link to see the talks). I’ve blogged last year about this field, which was driven by two remarkable experimental papers from Pablo Jarillo-Herrero’s group at MIT that came out around March. They found that two sheets of graphene, twisted relative to one another by about 1 degree, showed signed of strong electron correlation and superconductivity as a result of an effective long-wavelength superlattice created by the moiré interference pattern of the two slightly mismatched atomic potentials. The results were very impressive, but would this be a one-time success, or would it signal a nascent area of research?

Now 9 months later, it’s clear that the initial discovery has indeed given birth to a vibrant and promising field. At least 6 more leading experimental groups have observed correlation physics in similar moiré structures, and their progress is both impressive and inspiring. There are many observations of superconductivity, and now correlated insulators have been discovered at every integer “filling” of the moiré superlattice. Several groups showed measurements indicating apparent ferromagnetism or metamagnetism in the vicinity of the “1/4 filling” insulators, and furthermore signs that these states may be topologically non-trivial Chern insulators — i.e. they may possess a quantized Hall effect and edge states. This might even coexist with superconductivity.

Other measurements explored the electrical transport at temperatures above these ordering instabilities, finding evidence for a large T-linear component of the resistivity: with a slope 100 times larger than in untwisted graphene. The origin and significance of this was robustly debated. I was struck by the wealth of data from some of these experiments: a full measurement of the resistivity over a range of electron densities spanning two entire bands, and over a range of temperatures covering the full bandwidth (and more)! I can’t recall seeing anything quite like it. It reminds me of the idea, which arose in ultra-cold atomic physics, or doing “precision many body theory”. Understanding these volumes of data in quantitative detail may be a similar challenge in the solid state.

Being a theory institute, we saw of course a wide range of theoretical contributions presented and discussed. It’s clear that in this short time the field is already passing into a more refined stage. The initial furor of discovery is past and the opportunity for “quick and dirty” theory is passing with it. Theorists now must get serious and contend with the realities of this fascinating class of structures. There are many questions. A few that come to mind: What exactly are the implications of “fragile topology” here? How important are asymmetries induced by the realities of the devices? Which phenomena are due to phonons, and which phonons exactly? How much can the models for these systems really be simplified?

For definitive answers, I expect theory to need to get quantitative, and to confront directly the measured quantities like resistivity and its temperature, field, density dependence. A lot of the attendees are working towards this, and I am optimistic we will see major progress in the near future. More moiré measurements and theory is indeed better!

# Dirac points: the movie

There’s a lot of excitement about twisted bilayer graphene, which I wrote a bit about earlier.  We have been going back to basics and studying the band structure of these systems, using some of the models which have been largely accepted, at least in broad terms, to describe them.  These models take the form of two continuum coupled Dirac equations with a spatially periodic hopping term connecting them.  The first thorough early study was by Bistritzer and MacDonald back in 2011.  They discovered that (1) for nearly all angles the original Dirac points of persist, (2) at certain “magic” angles the Dirac velocity vanishes, and (3) near these magic angles the low energy bands become exceptionally narrow over the entire Brillouin zone.

What we showed in our recent preprint is that actually the vanishing Dirac velocity is just one of several topological phase transitions associated with merging/splitting/annihilation of Dirac points as the angle is varied.  The above video shows how these points move around the moiré Brillouin zone as the angle is varied, in a range of angles close to the first magic angle (about 1 degree).  The parameter $\alpha$ shown at the upper right of the video is inversely proportional to the angle.  Please see our preprint for more details.