Generalized harmonic confinement of massless Dirac fermions in (2+ 1) dimensions

TL;DR

This paper explores a method of confining massless Dirac fermions in two spatial dimensions using smooth magnetic fields, revealing conditions for confinement and providing exact solutions for energy states.

Contribution

It introduces a generalized harmonic confinement approach with specific magnetic field configurations, offering exact solutions for both zero and non-zero energy states.

Findings

Confinement occurs only at specific angular momentum values.

Exact solutions for energy states are derived.

Magnetic field configurations enable conditional confinement.

Abstract

In this article we discuss generalized harmonic confinement of massless Dirac fermions in (2+1) dimensions using smooth finite magnetic fields. It is shown that these types of magnetic fields lead to conditional confinement, that is confinement is possible only when the angular momentum (and parameters which depend on it) assumes some specific values. The solutions for non zero energy states as well as zero energy states have been found exactly.