Two-dimensional Dirac fermions in a mass superlattice

TL;DR

This paper investigates the behavior of 2D Dirac fermions in a periodic mass superlattice, revealing exact solutions for their dispersion, boundary, and interface modes, with implications for conductance and electronic properties.

Contribution

It provides exact analytical results for Dirac fermions in a mass superlattice, including dispersion relations and boundary mode characteristics, advancing understanding of topological and electronic phenomena.

Findings

Exact dispersion relations for Bloch and boundary modes.

Identification of interface modes sensitive to potential steps.

Prediction of conductance dependence on step position.

Abstract

We study two-dimensional (2D) Dirac fermions in the presence of a periodic mass term alternating between positive and negative values along one direction. This scenario could be realized for a graphene monolayer or for the surface states of topological insulators. The low-energy physics is governed by chiral Jackiw-Rebbi modes propagating along zero-mass lines, with the energy dispersion of the Bloch states given by an anisotropic Dirac cone. By means of the transfer matrix approach, we obtain exact results for a piece-wise constant mass superlattice. On top of Bloch states, two different classes of boundary and/or interface modes can exist in a finite-size geometry or in a nonuniform electrostatic potential, respectively. We compute the dispersion relation for both types of boundary and interface modes, which originate either from states close to the superlattice Brillouin zone (BZ) center or, via a Lifshitz transition, from states near the BZ boundary. In the presence of a potential step, we predict that the interface modes, the Bloch wave functions, and the electrical conductance will sensitively depend on the step position relative to the mass superlattice.