Tunelamento de Klein através de uma barreira dependente do tempo

Abstract

In this work, we studied how a wave packet describing a massless Dirac fermion representing a low-energy electron in graphene, behaves when it tunnels through a time dependent potential barrier. We investigate how the energy and probability density of this package changes when going through such a barrier. For this purpose, we use the Split-Operator method, which allows us to separately apply the terms due the potential and kinetic energies in the time evolution operator. With this, the kinetic energy part is solved analytically, while the potential energy part is applied to the wave function in a trivial way. Our results show that wave packet undergoing Klein tunneling through the potential barrier acquires an additional phase that, in our case, depends on time. Thus, considering a wave packet scattering on a barrier which depends linearly on time, it is shown that this phase eventually changes the final energy of the wave packet. This enables us to control the energy of the electron that propagates in graphene by simply adjusting the width and rate of change of potential in time.