Anomalous Electrodynamics and Quantum Geometry in a Graphene Heterobilayer.

Graphene heterobilayers with layer antisymmetric strains are studied using the Dirac-Harper model which describes a pair of single layer Dirac Hamiltonians coupled by a matrix-valued one-dimensional moir\'e-periodic interlayer potential. We find that this model hosts low energy, nearly dispersionless bands near charge neutrality that support anomalous polarizations of multipole distributions of the charge density. These are studied by formulating symplectic two-forms that encode field-induced multipole dynamics allowed in a chiral medium with time reversal symmetry. The model identifies reciprocity relations between the responses to layer-symmetric and layer-antisymmetric in-plane electric fields and reveals momentum-space quantum oscillations that can quantify the structure of its laterally modulated band inversions.