Dirac Fermions in Inhomogeneous Magnetic Field

TL;DR

This paper investigates the behavior of Dirac fermions in inhomogeneous magnetic fields, analyzing their energy spectra, reflection, transmission, and Klein paradox phenomena, with generalizations to gapped systems.

Contribution

It provides a detailed analysis of Dirac fermions in inhomogeneous magnetic fields, including energy spectra, reflection/transmission coefficients, and Klein paradox, extending to systems with energy gaps.

Findings

Derived energy spectrum solutions for Dirac fermions in inhomogeneous fields

Analyzed reflection and transmission coefficients and probability conditions

Discussed Klein paradox and current-carrying states in the system

Abstract

We study a confined system of Dirac fermions in the presence of inhomogeneous magnetic field. Splitting the system into different regions, we determine their corresponding energy spectrum solutions. We underline their physical properties by considering the conservation energy where some interesting relations are obtained. These are used to discuss the reflexion and transmission coefficients for Dirac fermions and check the probability condition for different cases. We generalize the obtained results to a system with gap and make some analysis. After evaluating the current-carrying states, we analyze the Klein paradox and report interesting discussions.