Electronic properties of bilayer graphene with magnetic quantum structures studied using the Dirac equation

TL;DR

This paper analytically investigates the electronic properties of bilayer graphene with magnetic quantum structures, revealing unique energy evolution behaviors, angular momentum transitions, and the Aharonov--Bohm effect.

Contribution

It provides an analytical solution to quasiparticle states in bilayer graphene with magnetic quantum dots and rings, highlighting novel energy and angular momentum phenomena.

Findings

Eigenstates change stepwise due to energy anticrossing.

Quantum states approach zero energy in certain conditions.

Aharonov--Bohm effect observed in eigenenergy spectra.

Abstract

The electronic properties of bilayer graphene with a magnetic quantum dot and a magnetic quantum ring are investigated. The eigenenergies and wavefunctions of quasiparticle states are calculated analytically by solving decoupled fourth-order differential equations. For the magnetic quantum dot, in the case of a negative inner magnetic field, two peculiar characteristics of the eigenenergy evolution are found: (i) the energy eigenstates change in a stepwise manner owing to energy anticrossing and (ii) the quantum states approach zero energy. For the magnetic quantum ring, there is an angular momentum transition of eigenenergy as the inner radius of the ring varies, and the Aharonov--Bohm effect is observed in the eigenenergy spectra for both positive and negative magnetic fields inside the inner radius.