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

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.

arXiv comment15 pages, 5 figures

References in corpus (18)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Universal Dynamic Conductivity and Quantized Visible Opacity of Suspended Graphene
• Pseudospin Magnetism in Graphene
• Pseudospin valve in bilayer graphene: towards graphene-based pseudospintronics
• Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order
• Pseudospin-driven spin relaxation mechanism in graphene
• On a solution of the Schrodinger equation with a hyperbolic double-well potential
• Test of Pseudospin Symmetry in Deformed Nuclei
• An approximate κ state solutions of the Dirac equation for the generalized Morse potential under spin and pseudospin symmetry
• Bound state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry
• Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields
• Magnetic quantum dots and rings in two dimensions
• Conductivity of graphene in the framework of Dirac model: Interplay between nonzero mass gap and chemical potential
• Logarithmic correction of the BTZ black hole and adaptive model of Graphene
• Electronic Structure in Gapped Graphene with Coulomb Potential
• Bound States in Gapped Graphene with Impurities : Effective Low-Energy Description of Short-Range Interactions
• Two-electron atom with a screened interaction

Cited by in corpus (4)

• Degeneracy and coherent states of the two-dimensional Morse potential
• Massive Dirac particles based on gapped graphene with Rosen-Morse potential in a uniform magnetic field
• SUSY partners and $S$-matrix poles of the one dimensional Rosen-Morse II Hamiltonian
• Coherent states of the two-dimensional non-separable supersymmetric Morse potential