Bilayer graphene in magnetic fields generated by supersymmetry

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 Schrödinger 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.

In this new version of the work, we correct the current density expression as well as some plots and include a new appendix to explain how to obtain the right form of the current density for bilayer graphene interacting with magnetic fields