Waveguiding in massive two-dimensional Dirac systems

TL;DR

This paper investigates waveguiding modes in gapped two-dimensional Dirac materials, deriving exact solutions and analyzing how potential parameters influence bound states and propagating modes for device applications.

Contribution

It extends previous work on pristine graphene by deriving exact solutions for waveguides in gapped Dirac systems with secant-hyperbolic potentials, considering effects of gaps and potential parameters.

Findings

Number of bound states depends on potential width, depth, and gap size.

Exact solutions involve Heun polynomials for gapped graphene.

Manipulating potential parameters controls propagating modes.

Abstract

The study of waveguide propagating modes is essential for achieving directional electronic transport in two-dimensional materials. Simultaneously, exploring potential gaps in these systems is crucial for developing devices akin to those employed in conventional electronics. Building upon the theoretical groundwork laid by Hartmann et al., which focused on implementing waveguides in pristine graphene monolayers, this work delves into the impact of a waveguide on two-dimensional gapped Dirac systems. We derive exact solutions encompassing wave functions and energy-bound states for a secant-hyperbolic attractive potential in gapped graphene, with a gap generated by sublattice asymmetry or a Kekul\'e-distortion. These solutions leverage the inherent properties and boundary conditions of the Heun polynomials. Our findings demonstrate that the manipulation of the number of accessible energy-bound states, i.e., transverse propagating modes, relies on factors such as the width and depth of the potential as well as the gap value of the two-dimensional material.