Energy spectrum of massive Dirac particles in gapped graphene with Morse potential

Z. Zali; Alireza Amani; J. Sadeghi; B. Pourhassan

doi:10.1016/j.physb.2021.413045

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arXiv · 2104.06725

Energy spectrum of massive Dirac particles in gapped graphene with Morse potential

Z. Zali·Alireza Amani·J. Sadeghi·B. Pourhassan

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Abstract

In this paper, we study the massive Dirac equation with the presence of the Morse potential in polar coordinate. The Dirac Hamiltonian is written as two second-order differential equations in terms of two spinor wavefunctions. Since the motion of electrons in graphene is propagated like relativistic fermionic quasi-particles, then one is considered only with pseudospin symmetry for aligned spin and unaligned spin by arbitrary $k$. Next, we use the confluent Heun's function for calculating the wavefunctions and the eigenvalues. Then, the corresponding energy spectrum obtains in terms of $N$ and $k$. Afterward, we plot the graphs of the energy spectrum and the wavefunctions in terms of $k$ and $r$, respectively. Moreover, we investigate the graphene band structure by a linear dispersion relation which creates an energy gap in the Dirac points called gapped graphene. Finally, we plot the graph of the valence and conduction bands in terms of wavevectors.

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Z. Zali, Alireza Amani, J. Sadeghi, B. Pourhassan. 2021-04-14. Energy spectrum of massive Dirac particles in gapped graphene with Morse potential. https://doi.org/10.1016/j.physb.2021.413045

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