# Moir\'e band model and band gaps of graphene on hexagonal boron nitride

## TL;DR

This paper develops a moiré band model for graphene on hexagonal boron nitride, analyzing how symmetry and strain influence band gaps and pseudomagnetic fields, with implications for electronic properties.

## Contribution

The paper introduces a comprehensive moiré band model for G/BN that incorporates symmetry and ab-initio data, elucidating the origins of primary and secondary Dirac point gaps.

## Key findings

- Moiré patterns induce primary Dirac point gaps via inversion symmetry breaking.
- Secondary gaps arise from specific pseudospin component mixing.
- Pseudomagnetic fields up to 40 Tesla are mainly due to virtual hopping.

## Abstract

Nearly aligned graphene on hexagonal boron nitride (G/BN) can be accurately modeled by a Dirac Hamiltonian perturbed by smoothly varying moir\'e pattern pseudospin fields. Here, we present the moir\'e-band model of G/BN for arbitrary small twist angles under a framework that combines symmetry considerations with input from ab-initio calculations. Our analysis of the band gaps at the primary and secondary Dirac points highlights the role of inversion symmetry breaking contributions of the moir\'e patterns, leading to primary Dirac point gaps when the moir\'e strains give rise to a finite average mass, and to secondary gaps when the moir\'e pseudospin components are mixed appropriately. The pseudomagnetic strain fields which can reach values of up to $\sim$40 Tesla near symmetry points in the moir\'e cell stem almost entirely from virtual hopping and dominate over the contributions arising from bond length distortions due to the moir\'e strains.