Electron in bilayer graphene with magnetic fields leading to shape invariant potentials

TL;DR

This paper investigates the quantum behavior of electrons in bilayer graphene under magnetic fields by applying supersymmetric quantum mechanics to derive analytical solutions for bound states and analyze their spectra.

Contribution

It introduces a method using second-order supersymmetric quantum mechanics to find shape invariant potentials and analytical energy solutions in bilayer graphene with magnetic fields.

Findings

Analytical solutions for bound states in specific magnetic fields

Spectrum analysis of electron states in bilayer graphene

Determination of probability and current densities

Abstract

The quantum behavior of electrons in bilayer graphene with applied magnetic fields is addressed. By using second-order supersymmetric quantum mechanics the problem is transformed into two intertwined one dimensional stationary Schr\"odinger equations whose potentials are required to be shape invariant. Analytical solutions for the energy bound states are obtained for several magnetic fields. The associated spectrum is analyzed, and the probability and current densities are determined.