Klein paradox for arbitrary spatio-temporal scalar potential and Josephson-like current in graphene

Details Klein paradox for arbitrary spatio-temporal scalar potential and Josephson-like current in graphene Klein paradox for arbitrary spatio-temporal scalar potential and Josephson-like current in graphene

2011-07-25

arxiv.org/abs/1107.4983v1

Physics

Condensed Matter

Materials Science

5 pages, 1 figure

Scientific paper

We derive the exact time evolution according to the Dirac-Weyl equation, describing a mono-layer of graphene, in the presence of a scalar potential U(x,t) of arbitrary spatial and temporal dependence at normal incidence, p_y=0. This solution shows that the Klein paradox (the absence of backscattering) persists even for arbitrary temporal modulations of the barrier. Moreover, we identify an unusual oscillating current j_y running along the barrier, despite of the vanishing momentum in y-direction. This current exhibits resemblence to the Josephson current in superconductors, including the occurance of Shapiro steps and its sine-like dependence on the phase difference of wave functions.

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