Exact analytic solutions for a Dirac electron moving in graphene under magnetic fields

Abstract

Exact analytical solutions for the bound states of a graphene Dirac electron in various magnetic fields with translational symmetry are obtained. In order to solve the time-independent Dirac-Weyl equation the factorization method used in supersymmetric quantum mechanics is adapted to this problem. The behavior of the discrete spectrum, probability and current densities are discussed.

Pseudo Hermitian Interactions in the Dirac Equation

“…Note that for α = 0, we get back the results of [8,24]. Using Equation (18) in the second half of Equation (7), we find:…”

Graphene nanoribbon in sharply localized magnetic fields

“…Specifically, we take B(x) =ẑB 0 sech 2 (µx) (Fig. 5) [20,21], where B 0 is the strength of the field and µ −1 stands for its range. The corresponding vector potential (Fig.…”

Quasi-exact solution to the Dirac equation for the hyperbolic-secant potential

“…It has been shown that it is possible to confine graphene electrons by electrostatic potentials [16][17][18][19][20][21][22][23][24][25][26][27][28], magnetic barriers [29][30][31][32][33][34][35][36][37][38][39], and straininduced fields [40][41][42][43]. Transmission through symmetric [15][16][17][18]27,28,32,[44][45][46][47][48][49][50][51][52][53][54][55][56] and asymmetric electrostatic barriers [25] have been studied and fully confined modes within a smooth one-dimensional potential have been predicted to exist at zero energy …”