Exact solution of the Dirac–Weyl equation in graphene under electric and magnetic fields - 07/01/17

Doi : 10.1016/j.crhy.2016.06.002

Mahdi Eshghi ^a,^b,^{^⁎} , Hosein Mehraban ^a
^a Faculty of Physics, Semnan University, Semnan, Iran
^b Department of Physics, Imam Hosein Comprehensive University, Tehran, Iran

^⁎Corresponding author at: Department of Physics, Imam Hosein Comprehensive University, Tehran, Iran.Department of PhysicsImam Hosein Comprehensive UniversityTehranIran

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Abstract

In this paper, we have obtained exact analytical solutions for the bound states of a graphene Dirac electron in magnetic fields with various q-parameters under an electrostatic potential. In order to solve the time-independent Dirac–Weyl equation, the Nikoforov–Uvarov (NU) and Frobenius methods have been used. We have also investigated the thermodynamic properties by using the Hurwitz zeta function method for one of the states. Finally, some of the numerical results are also shown.

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Keywords : Graphene, Dirac–Weyl equation, Nikoforov–Uvarov method