Weyl Fermions in a 2+1 Dimensional Optical Background of Constant Negative Curvature

Abstract

In this manuscript, we try to analyse the evolution of a Weyl particle in a 2+1 dimensional optical background of constant negative curvature. This background was introduced through determining the optical Banados-Teitelboim-Zanelli metric, and it is quite similar to 2+1 dimensional hyperbolic wormhole. In order to analyse the effects of this background on the evolution of the massless fermions, we start with by setting up the corresponding Dirac equation. We show that this equation can be reduced into an exactly soluble form and accordingly we obtain an expression for the relativistic frequency modes of the system. We observe that these modes decay in time without any real oscillation and the damped modes depend explicitly on the parameters of the background. Our results imply that tunnelling time of a charge carrier in a graphene wormhole can be controlled through adjusting the radius of curvature of the wormhole connecting the sheets, in principle.