Bilayer graphene in magnetic fields generated by supersymmetry

TL;DR

This paper uses supersymmetric quantum mechanics to solve the effective Hamiltonian of bilayer graphene in magnetic fields, generating new magnetic field configurations and analyzing their spectral and physical properties.

Contribution

It introduces a novel application of second-order SUSY quantum mechanics to bilayer graphene, creating new magnetic field profiles beyond shape-invariant potentials.

Findings

New magnetic field configurations are analytically derived.

Spectral properties of the generated fields are characterized.

Probability and current densities are analyzed for these solutions.

Abstract

The effective Hamiltonian for electrons in bilayer graphene with applied magnetic fields is solved through second-order supersymmetric quantum mechanics. This method transforms the corresponding eigenvalue problem into two intertwined one dimensional stationary Schr\"odinger equations whose potentials are determined by choosing at most two seed solutions. In this paper new kinds of magnetic fields associated to non-shape-invariant SUSY partner potentials are generated. Analytic solutions for these magnetic fields are found, the associated spectrum is analyzed, and the probability and current densities are explored.