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Berlin 2012 – scientific programme

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HL: Fachverband Halbleiterphysik

HL 78: Transport: Graphene 1 (jointly with TT, MA, DY, DS, O)

HL 78.9: 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 grapheneSergey E. Savel’ev1, •Wolfgang Häusler2, and Peter Hänggi21Department 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, py=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 jy 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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