Construction of zero energy states in graphene through the supersymmetry formalism

TL;DR

This paper introduces a supersymmetry-based approach to construct zero-energy states in graphene, specifically for a 2D massless Dirac equation with hyperbolic scalar potentials, enabling the design of experimentally feasible interactions.

Contribution

It presents a novel supersymmetry formalism for generating zero-energy states in graphene, expanding the toolkit for manipulating Dirac fermions in two-dimensional materials.

Findings

Successfully constructs supersymmetric partners of the Dirac system.

Derives a reality condition for the transformed potentials.

Potential applications in approximating experimentally realizable interactions.

Abstract

We devise a supersymmetry-based method for the construction of zero-energy states in graphene. Our method is applied to a two-dimensional massless Dirac equation with a hyperbolic scalar potential. We determine supersymmetric partners of our initial system and derive a reality condition for the transformed potential. The Dirac potentials generated by our method can be used to approximate interactions that are experimentally realizable.