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

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