I’ve taken too long of a hiatus from writing here.Â 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 MoirĂ© 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 moirĂ© 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 moirĂ© 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 moirĂ© 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 moirĂ© measurements and theory is indeed better!