The low-energy bands of twisted bilayer graphene form Dirac cones with approximate electron-hole symmetry at small rotation angles. These crossings are protected by the emergent symmetries of long moiré patterns, conferring a nontrivial topological character upon the bands. Different strain fields on the two layers (heterostrain) shift the Dirac points both in energy and momentum. The overlap of conduction and valence bands favors an excitonic instability of the Fermi surface close to the neutrality point. The condensate breaks time reversal symmetry and the separate conservation of charge in each valley. The order parameter describes interlayer circulating currents giving rise to a Kekulé-like orbital magnetization density wave. Vortices in this order parameter carry fermion numbers owing to the underlying topology of the bands. This mechanism may explain the occurrence of insulating states at neutrality in the most homogenous samples, where uniform strain fields contribute both to stabilizing the relative orientation between layers and to the formation of an excitonic gap.

Hector Ochoa

Columbia University