Josephson-like currents in graphene for arbitrary time-dependent potential barriers

摘要

From the exact solution of the Dirac-Weyl equation we find unusual currentsj_y running in y-direction parallel to a time-dependent scalar potentialbarrier W(x,t) placed upon a monolayer of graphene, even for vanishing momentumcomponent p_y. In their sine-like dependence on the phase difference of wavefunctions, describing left and right moving Dirac fermions, these currentsresemble Josephson currents in superconductors, including the occurance ofShapiro steps at certain frequencies of potential oscillations. TheJosephson-like currents are calculated for several specific time-dependentbarriers. A novel type of resonance is discovered when, accounting for theFermi velocity, temporal and spatial frequencies match.