Abstract: Placing a two-dimensional lattice with a small rotation gives rise to almost periodic "moiré" patterns on a superlattice scale much larger than the original lattice. We have used the mathematical techniques developed to study waves in inhomogeneous media to identify a regime where the Bistritzer-MacDonald continuum model emerges as the effective dynamics for electrons modeled as wave-packets spectrally concentrated at the monolayer Dirac points of linear dispersion, up to error that we rigorously estimate. We have shown that this regime is realized in twisted bilayer graphene at the first "magic" angle where the group velocity of the wave packet is zero and strongly correlated electronic phases (superconductivity, Mott insulators, etc.) have recently been observed.

We will present recent results that rigorously extend this analysis to account for the effects of structural relaxation and to essentially arbitrary moiré materials such as twisted multilayer transition metal dichalcogenides (TMDs) or even twisted heterostructures consisting of layers of distinct 2D materials.

Contact: Ian Tobasco