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

• URL: http://arxiv.org/abs/2104.06725v1
• Date: Wed, 14 Apr 2021 09:26:56 GMT
• Title: Energy spectrum of massive Dirac particles in gapped graphene with Morse potential
• Authors: Z.Zali, Alireza Amani, J.Sadeghi, B.Pourhassan
• Abstract summary: 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. We investigate the graphene band structure by a linear dispersion relation which creates an energy gap in the Dirac points called gapped graphene.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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