Bound states in inhomogeneous magnetic field in graphene: a semiclassical approach

TL;DR

This paper develops a semiclassical method to analyze bound states in graphene under inhomogeneous magnetic fields, highlighting the role of a semiclassical phase and validating results with quantum and numerical calculations.

Contribution

It introduces semiclassical quantization equations for graphene in magnetic fields, emphasizing the semiclassical phase due to spinor properties, and confirms their accuracy against quantum and numerical methods.

Findings

Semiclassical eigenenergies agree with quantum Dirac equation results.

The semiclassical phase is crucial due to the spinor nature of graphene excitations.

The approach provides a reliable approximation for bound states in inhomogeneous magnetic fields.

Abstract

We derive semiclassical quantization equations for graphene mono- and bilayer systems where the excitations are confined by the applied inhomogeneous magnetic field. The importance of a semiclassical phase, a consequence of the spinor nature of the excitations, is pointed out. The semiclassical eigenenergies show good agreement with the results of quantum mechanical calculations based on the Dirac equation of graphene and with numerical tight binding calculations.