Non-hermitian Dirac Hamiltonian in the presence of local Fermi velocity

TL;DR

This paper introduces a novel method to analyze non-Hermitian (1+1)-dimensional Dirac Hamiltonians with local Fermi velocity, solving for both PT-symmetric and non-PT-symmetric potentials using the Nikiforov-Uvarov approach.

Contribution

It applies the Nikiforov-Uvarov method to solve non-Hermitian Dirac systems with local Fermi velocity, exploring PT-symmetric and non-PT-symmetric potential classes.

Findings

Solved harmonic oscillator with linear vector potential in PT-symmetric case

Solved shifted harmonic oscillator in non-PT-symmetric case

Demonstrated solvability of non-Hermitian Dirac Hamiltonians with local Fermi velocity

Abstract

We present a new approach to study a class of non-Hermitian (1+1)-dimensional Dirac Hamiltonian in the presence of local Fermi velocity. We apply the well known Nikiforov-Uvarov method to solve such a system. We discuss applications and explore the solvability of both $\mathcal{PT}$-symmetric and non-$\mathcal{PT}$ symmetric classes of potentials. In the former case we obtain the solution of a harmonic oscillator in the presence of a linear vector potential while in the latter case we solve the shifted harmonic oscillator problem.