Exploring Massive Dirac Particles in Gapped Graphene Structures

Recent research by A. Kalani, Alireza Amani, and M. A. Ramzanpour explores the behavior of massive Dirac particles in a gapped graphene structure under the influence of a Rosen-Morse potential and a uniform magnetic field. The study, titled "Massive Dirac particles based on gapped graphene with Rosen-Morse potential in a uniform magnetic field," was submitted to arXiv on August 30, 2024.

The authors investigate how electrons in graphene can be modeled as relativistic fermion quasi-particles, utilizing the Dirac equation to analyze their wave functions. They derive eigenvalues and eigenvectors through the Legendre differential equation, which allows them to determine the energy levels of the system. The research highlights the energy spectrum for both the ground state and the first excited state, providing insights into the bounded states of energy influenced by the coefficients of the Rosen-Morse and magnetic potentials.

Additionally, the authors examine the band structure of gapped graphene, presenting a modified dispersion relation expressed in terms of two-dimensional wave vectors. The findings include plots of the energy bands with and without the magnetic term, contributing to a deeper understanding of the electronic properties of gapped graphene.

This research could have implications for the development of advanced materials and devices that leverage the unique properties of graphene, particularly in the fields of quantum computing and nanotechnology. The work is available for further review at arXiv:2409.00234.