Factorization of Dirac Equation and Graphene Quantum Dot

TL;DR

This paper investigates the Dirac equation in a graphene quantum dot with various potential configurations, demonstrating bound states with a mass term and analyzing scattering properties.

Contribution

It introduces a method to analyze Dirac equation solutions in quantum dots with different potentials, highlighting conditions for bound states and scattering characteristics.

Findings

Bound states exist with a mass term in electrostatically confined quantum dots.

Differential cross section depends on potential parameters.

Potential configurations influence quantum dot confinement and scattering behavior.

Abstract

We consider a quantum dot described by a cylindrically symmetric 2D Dirac equation. The potentials representing the quantum dot are taken to be of different types of potential configuration, scalar, vector and pseudo-scalar to enable us to enrich our study. Using various potential configurations, we found that in the presence of a mass term an electrostatically confined quantum dot can accommodate true bound states, which is in agreement with previous work. The differential cross section associated with one specific potential configuration has been computed and discussed as function of the various potential parameters.