On the confinement of a quantum particle to a two-dimensional ring in systems described by the Dirac equation

TL;DR

This paper introduces a novel minimal coupling in the Dirac equation to model the confinement of a spin-half particle in a two-dimensional quantum ring, extending previous non-relativistic models to relativistic systems.

Contribution

It presents a new minimal coupling approach in the Dirac equation to generalize quantum ring confinement models for relativistic particles.

Findings

Generalizes non-relativistic quantum ring models to relativistic particles

Provides a new framework for studying relativistic quantum confinement

Extends the model by Tan and Inkson to Dirac particles

Abstract

In this contribution, we propose a new model for studying the confinement of a spin-half particle to a two-dimensional quantum ring in systems described by the Dirac equation by introducing a new minimal coupling into the Dirac equation. We show that the introduction of this new minimal coupling into the Dirac equation yields a generalization of the two-dimensional model for a quantum ring proposed by Tan and Inkson [W.-C. Tan and J. C. Inkson, Semicond. Sci. Technol. {\bf11}, 1635 (1996)] for relativistic spin-half quantum particles.