Dirac-Harper Theory for One Dimensional Moir\'e Superlattices

TL;DR

This paper develops a Dirac Harper model to analyze one-dimensional moiré superlattices, revealing low-energy spectra with weakly dispersive bands and exploring their charge and valley properties through symmetry analysis.

Contribution

It introduces a novel Dirac Harper framework for 1D moiré superlattices, combining discrete and continuum approaches to uncover hierarchical band structures and symmetry-based charge distributions.

Findings

Identification of weakly dispersive low-energy bands

Analysis of charge distributions and valley coherence

Use of symmetry principles to understand mode structure

Abstract

We study a Dirac Harper model for moir\'e bilayer superlattices where layer antisymmetric strain periodically modulates the interlayer coupling between two honeycomb lattices in one spatial dimension. Discrete and continuum formulations of this model are analyzed. For sufficiently long moir\'e period the we find low energy spectra that host a manifold of weakly dispersive bands arising from a hierarchy of momentum and position dependent mass inversions. We analyze their charge distributions, mode count and valley-coherence using exact symmetries of the lattice model and approximate symmetries of a four-flavor version of the Jackiw-Rebbi one dimensional solution.