(1+1)-Dirac bound states in one-dimension; position-dependent Fermi velocity and mass

TL;DR

This paper investigates bound states of one-dimensional Dirac particles with position-dependent mass and velocity, revealing conditions for bound states including bound states in the continuum, and explores specific models like Poschl-Teller and harmonic oscillator.

Contribution

It extends previous work by analyzing Dirac particles with both position-dependent mass and velocity, identifying conditions for bound states including BIC-like solutions.

Findings

Bound states exist for Dirac particles with position-dependent mass and velocity.

BIC-like solutions are feasible under specific conditions on mass and velocity.

Poschl-Teller and harmonic oscillator models are successfully applied.

Abstract

We extend Panella and Roy's [13] work on one-dimensional heterostructure for massless Dirac particles with position-dependent (PD) velocity. We consider Dirac particles where both the mass and velocity are position-dependent. Bound states in the continuum (BIC)-like and discrete bound state solutions are reported. It is observed that BIC-like solutions are not only feasible for the ultra-relativistic (massless) Dirac particles but also for Dirac particles with PD-mass and PD-velocity that satisfy the condition m(x)v(x)v(x)=A, where A is constant. (1+1)-Dirac Poschl-Teller and harmonic oscillator models are also reported.