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

TL;DR

This paper uncovers Josephson-like currents in graphene induced by arbitrary time-dependent potential barriers, revealing novel resonances and behaviors analogous to superconducting Josephson effects.

Contribution

It provides an exact solution to the Dirac-Weyl equation showing how time-dependent barriers generate Josephson-like currents in graphene, a novel phenomenon.

Findings

Josephson-like currents occur even at zero momentum component p_y.

Resonance phenomena emerge when temporal and spatial frequencies match.

Shapiro steps are observed at specific oscillation frequencies.

Abstract

From the exact solution of the Dirac-Weyl equation we find unusual currents j_y running in y-direction parallel to a time-dependent scalar potential barrier W(x,t) placed upon a monolayer of graphene, even for vanishing momentum component p_y. In their sine-like dependence on the phase difference of wave functions, describing left and right moving Dirac fermions, these currents resemble Josephson currents in superconductors, including the occurance of Shapiro steps at certain frequencies of potential oscillations. The Josephson-like currents are calculated for several specific time-dependent barriers. A novel type of resonance is discovered when, accounting for the Fermi velocity, temporal and spatial frequencies match.