Graphene nanoribbon in sharply localized magnetic fields

Abstract

We study the effect of a sharply localized magnetic field on the electron transport in a strip (ribbon) of graphene sheet, which allows to give results for the transmission and reflection probability through magnetic barriers. The magnetic field is taken as a single and double delta type localized functions, which are treated later as the zero width limit of gaussian fields. For both field configurations, we evaluate analytically and numerically their transmission and reflection coefficients. The possibility of spacial confinement due to the inhomogeneous field configuration is also investigated.

Supersymmetric analysis of the Dirac-Weyl operator within $\mathcal{PT}$PT symmetry

“…There have been many studies on various theoretical as well as experimental aspects of graphene. For example, a series of studies concerning the interaction of graphene electrons in perpendicular magnetic fields [7,8,9,10], position dependent Fermi velocity and analytical solutions [11,12,13], chiral symmetry breaking in graphene [14], exact solutions of the (2 + 1) dimensional spacetime Dirac equation within minimal length [15]. Moreover, methods of the super-symmetric quantum mechanics are used to obtain analytical solutions for the massless Dirac electrons in spherical molecules [16], the Dirac equation in two dimensional curved space-time with Lie algebraic approach can be found in [17].…”