Position-dependent mass Dirac equation and local Fermi velocity

TL;DR

This paper investigates a (1+1)-dimensional Dirac equation with a position-dependent Fermi velocity and effective mass, revealing a key inverse square relationship and solving for various potentials.

Contribution

It introduces a novel approach linking effective mass and Fermi velocity in the Dirac equation, providing new solutions for different potential profiles.

Findings

Mass is inversely proportional to the square of Fermi velocity.

Derived solutions for free particle, harmonic oscillator, Morse, and CPRS potentials.

Established a new constraint relating mass and Fermi velocity.

Abstract

We present a new approach to study (1+1)-dimensional Dirac equation in the background of an effective mass $M$ by exploiting the possibility of a position-dependent fermi velocity $v_f$. We explore the resulting structure of the coupled equations and arrive at an interesting constraint of $M$ turning out to be the inverse square of $v_f$. We address several solutions of the effective potential that include the free particle, shifted harmonic oscillator, Morse potential, and CPRS potential.