Polar coherent states in bilayer graphene under a constant uniform magnetic field

TL;DR

This paper explores the symmetries, eigenfunctions, and coherent states of bilayer graphene in a magnetic field, revealing gauge-invariant properties and a novel radial interference effect in current densities.

Contribution

It introduces a new framework for defining coherent states in bilayer graphene and analyzes their properties using symmetry considerations and polar coordinates.

Findings

Symmetries explain the spectrum and pseudo-spin properties.

Gauge-invariant probability and current densities are derived.

Radial interference effects in local current densities are observed.

Abstract

Symmetries associated with the Hamiltonian describing bilayer graphene subjected to a constant magnetic field perpendicular to the plane of the bilayer are calculated using polar coordinates. These symmetries are then applied to explain some fundamental properties, such as the spectrum and the integer pseudo-spin character of the eigenfunctions. The probability and current densities of the bilayer Hamiltonian have also been calculated in polar coordinates and shown to be gauge invariant and scalar under generalized rotations. We also define appropriate coherent states of this system as eigenfunctions, with complex eigenvalues, of a suitable chose annihilation operator. In this framework, symmetries are also useful to show the meaning of the complex eigenvalue in terms of expected values. The local current density of these coherent states is shown to exhibit a kind of radial component interference effect, something that has gone unnoticed until now. Some of these results that have just been exposed are graphically illustrated throughout the manuscript.