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.