Massive Dirac particles based on gapped graphene with Rosen-Morse potential in a uniform magnetic field

TL;DR

This paper investigates the electronic properties of gapped graphene under Rosen-Morse potential and magnetic field, deriving energy spectra and wave functions using the Dirac equation, and analyzing band structures.

Contribution

It introduces a novel analysis of gapped graphene with Rosen-Morse potential in a magnetic field using relativistic Dirac formalism, deriving eigenvalues, eigenstates, and band structures.

Findings

Eigenvalues and eigenvectors obtained via Legendre differential equation.

Energy spectra calculated for ground and first excited states.

Band structures plotted with and without magnetic field.

Abstract

We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field. In order to describe the corresponding structure, we consider the propagation of electrons in graphene as relativistic fermion quasi-particles, and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation. Next, to solve and analyze the Dirac equation, we obtain the eigenvalues and eigenvectors using the Legendre differential equation. After that, we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal \(n\) and spin-orbit \(k\). Then, the values of the energy spectrum for the ground state and the first excited state are calculated, and the wave functions and the corresponding probabilities are plotted in terms of coordinates $r$. In what follows, we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors $K_x$ and $K_y$. Finally, the energy bands are plotted in terms of the wave vectors $K_x$ and $K_y$ with and without the magnetic term.