Berlin 2012 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 39: Transport: Graphene 1 (jointly with MA, HL, DY, DS, O)

TT 39.9: Talk

Thursday, March 29, 2012, 11:45–12:00, BH 334

Klein paradox for arbitrary spatio-temporal scalar potential barrier and Josephson-like current in graphene — Sergey E. Savel’ev¹, •Wolfgang Häusler², and Peter Hänggi² — ¹Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom — ²Institut für Physik Universität Augsburg, D-86135 Augsburg, Germany

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.