Soft modes of moiré patterns

We will start to answer the following question: What is the nature of the highly resistive metal observed in the system formed by two layers of carbon atoms with a small twist between them? The question is pertinent because this system becomes a superconductor at low temperatures; when the superconductivity is killed (by a magnetic field, for example) this highly resistive state survives down to very low temperatures, lower than any energy scale that we can think of. This behavior is akin to what happens in high-Tc superconductors and remains a big mystery in condensed matter physics.

"Conventional wisdom" dictates that this phenomenology is probably reminiscent of a quantum critical point at which the energy scales of the system vanish. Our philosophy will be different, though: The small twist makes the graphene layers incommensurate to each other, and that implies the existence of soft modes that could be very effective in scattering electrons. A first step in this research program is to understand quantitatively how these modes dissipate energy and momentum and become overdamped in the process. In practice, this means to compute the friction between the two graphene layers caused by anharmonic fluctuations with wavelengths smaller than the pitch of the associated moiré pattern represented in the figure.

Knowledge of solid state physics and programming skills (e.g., in Python/Julia) will come in handy, but the inescapable requisites are dedication and good sense of humor