Perturbative/nonperturbative aspects of Bloch electrons in a honeycomb lattice

TL;DR

This paper investigates the spectral properties of Bloch electrons in a honeycomb lattice under magnetic fields, revealing perturbative and nonperturbative features, and uncovering connections to supersymmetric quantum mechanics.

Contribution

It introduces a systematic framework for magnetic flux expansions and explores the nonperturbative spectrum, highlighting novel similarities to supersymmetric sine-Gordon models.

Findings

Perturbative flux expansions near band edges are systematically computed.

Nonperturbative bandwidth analysis reveals new spectral features.

A connection between honeycomb lattice spectra and supersymmetric quantum mechanics is established.

Abstract

We revisit the spectral problem for Bloch electrons in a two-dimensional bipartite honeycomb lattice under a uniform magnetic field. It is well-known that such a honeycomb structure is realized in graphene. We present a systematic framework to compute the perturbative magnetic flux expansions near two distinct band edges. We then analyze the nonperturbative bandwidth of the spectrum. It turns out that there is a novel similarity between the spectrum near the Dirac point in the honeycomb lattice and the spectrum in the supersymmetric sine-Gordon quantum mechanics. We finally confirm a nontrivial vacuum-instanton-bion threesome relationship. Our analysis heavily relies on numerical experiments.