Anomalous Electrodynamics and Quantum Geometry in the Dirac-Harper model for a Graphene Bilayer

TL;DR

This paper explores the effects of layer antisymmetric strains in graphene bilayers using a Dirac-Harper model, revealing anomalous charge polarization, a generalized Berry curvature, and momentum-space quantum oscillations due to moiré-scale band inversions.

Contribution

It introduces a novel Dirac-Harper model for strained graphene bilayers that uncovers anomalous polarization effects and a generalized Berry curvature related to moiré patterns.

Findings

Identification of nearly dispersionless bands near charge neutrality.

Discovery of anomalous charge multipole polarizations.

Observation of quantum oscillations from band inversions.

Abstract

Graphene bilayers with layer antisymmetric strains are studied using the Dirac-Harper model for a pair of single layer Dirac Hamiltonians coupled by a one-dimensional moir\'e-periodic interlayer tunneling amplitude. This model hosts low energy, nearly dispersionless bands near charge neutrality that support anomalous polarizations of its charge multipole distributions. These are analyzed introducing a generalized Berry curvature that encodes the field-induced dynamics of multipole fields allowed in a chiral medium with time reversal symmetry. The formulation identifies a reciprocity relation between responses to layer-symmetric and layer-antisymmetric in-plane electric fields and reveals momentum-space quantum oscillations produced by a spatial pattern of band inversions on the moir\'e scale.