Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields

TL;DR

This paper demonstrates how two-dimensional massless Dirac fermions can be confined using spatially varying magnetic fields, revealing confinement-deconfinement transitions and novel solvable models with potential applications in quantum materials.

Contribution

It introduces a new method for trapping Dirac fermions in inhomogeneous magnetic fields and presents a quasi-exactly solvable model using confluent Heun functions.

Findings

Successful confinement of Dirac fermions in magnetic quantum dots.

Identification of confinement-deconfinement transitions based on magnetic field modulation.

Development of a new solvable model using confluent Heun functions.

Abstract

We show how it is possible to trap two-dimensional massless Dirac fermions in spatially inhomogeneous magnetic fields, as long as the formed magnetic quantum dot (or ring) is of a slowly decaying nature. It is found that a modulation of the depth of the magnetic quantum dot leads to successive confinement-deconfinement transitions of vortexlike states with a certain angular momentum, until a regime is reached where only states with one sign of angular momentum are supported. We illustrate these characteristics with both exact solutions and a hitherto unknown quasi-exactly solvable model utilizing confluent Heun functions.