Pseudo-Hermitian Dirac operator on the torus for massless fermions under the action of external fields

TL;DR

This paper investigates the Dirac equation for massless fermions on a torus under external fields, employing pseudo-Hermitian operator theory and deriving analytical solutions for specific Fermi velocity profiles.

Contribution

It introduces a pseudo-Hermitian Dirac operator framework on a torus and provides analytical solutions for constant and variable Fermi velocities.

Findings

Analytical solutions for Dirac equation with constant Fermi velocity

Analytical solutions for Dirac equation with position-dependent Fermi velocity

Application of pseudo-Hermitian operator theory to curved 2D surfaces

Abstract

The Dirac equation in $(2+1)$ dimensions on the toroidal surface is studied for a massless fermion particle under the action of external fields. Using the covariant approach based on general relativity, the Dirac operator stemming from a metric related to the strain tensor is discussed within the Pseudo-Hermitian operator theory. Furthermore, analytical solutions are obtained for two cases, namely, constant and position-dependent Fermi velocity.