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.
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?
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.