Green functions of electrons in monolayer and bilayer graphene in a magnetic field

TL;DR

This paper derives explicit Green function expressions for electrons in monolayer and bilayer graphene under magnetic fields, using Whittaker functions, aiding in understanding their quantum behavior.

Contribution

It provides closed-form Green functions for electrons in graphene in magnetic fields, a novel analytical result for these systems.

Findings

Explicit Green functions expressed via Whittaker functions.

Analytical tools for studying electronic properties in graphene.

Facilitates further theoretical and computational research.

Abstract

Closed expressions for the Green functions of the stationary two-dimensional two-component Schrodinger equation for an electron moving in monolayer and bilayer graphene in the presence of a magnetic field are obtained in terms of the Whittaker functions.