Conditional electron confinement in graphene via smooth magnetic fields

TL;DR

This paper explores how smooth, finite magnetic fields can be used to confine electrons in graphene, providing exact solutions for bound states in both conditionally and quasi exactly solvable systems.

Contribution

It introduces new magnetic field configurations that enable exact solutions for electron confinement in graphene, advancing understanding of magnetic confinement techniques.

Findings

Exact bound state energies and wave functions obtained

Two types of magnetic fields analyzed: conditionally and quasi exactly solvable

Provides analytical solutions for electron confinement in graphene

Abstract

In this article we discuss confinement of electrons in graphene via smooth magnetic fields which are finite everywhere on the plane. We shall consider two types of magnetic fields leading to systems which are conditionally exactly solvable and quasi exactly solvable. The bound state energies and wave functions in both cases have been found exactly.