Non-Hermitian fermions with effective mass

TL;DR

This paper explores the quantum dynamics of non-Hermitian fermions with position-dependent mass in a 1+1D spacetime, revealing how different mass distributions influence effective potentials and particle behavior.

Contribution

It introduces a PT-symmetric Schrödinger-like framework for non-Hermitian fermions with PDM and analyzes specific mass profiles, including linear and hyperbolic cases.

Findings

Linear PDM yields an effective harmonic oscillator with bound states.

Hyperbolic PDM results in an effective potential barrier.

Fermions behave as free particles with positive energy in hyperbolic PDM.

Abstract

In this work, we readdress the Dirac equation in the position-dependent mass (PDM) scenario. Here, one investigates the quantum dynamics of non-Hermitian fermionic particles with effective mass assuming a $(1+1)$-dimension flat spacetime. In seeking a Schr\"{o}dinger-like theory with PT symmetry is appropriate to assume a complex potential. This imaginary interaction produces an effective potential purely dependent on mass distribution. Furthermore, we study the non-relativistic limit by adopting the Foldy-Wouthuysen transformation. As a result, that limit leads to an ordering equivalent to the ordering that describes abrupt heterojunctions. Posteriorly, particular cases of mass distribution also were analyzed. Thus, interesting results arise for the case of a linear PDM, which produces an effective harmonic oscillator and induces the emergence of bound states. For a hyperbolic PDM, an effective potential barrier emerges. However, in this case, the fermions behave as free particles with positive-defined energy.