Supersymmetric quantum electronic states in graphene under uniaxial strain

TL;DR

This paper investigates how uniaxial strain and non-uniform magnetic fields affect the electronic states in graphene, revealing supersymmetric structures and providing analytical solutions for wave functions and energy levels.

Contribution

It introduces a framework for analyzing supersymmetric quantum states in strained graphene under complex magnetic field profiles, with explicit analytical solutions.

Findings

Supersymmetric structures can emerge in strained graphene under specific magnetic conditions.

Analytical expressions for wave functions and energy eigenvalues are derived.

The results depend on magnetic field intensity and strain-induced anisotropy.

Abstract

We study uniaxially strained graphene under the influence of non-uniform magnetic fields perpendicular to the material sample with a coordinate independent strain tensor. For that purpose, we solve the Dirac equation with anisotropic Fermi velocity and explore the conditions upon which such an equation possesses a supersymmetric structure in the quantum mechanical sense through examples. Working in a Laudau-like gauge, wave functions and energy eigenvalues are found analytically in terms of the magnetic field intensity, the anisotropy scales and other relevant parameters that shape the magnetic field profiles.