Nanotech 2010

Critical currents in graphene ribbon Josephson junctions

P.G. Gabrielli

Keywords: graphene, critical current, Josephson junction


Most of the remarkable transport properties of graphene have to do with its particular band structure at low energies: the undoped system has a finite number of Fermi points, placed at the corner of the hexagonal Brillouin zone, and only two such points can be taken as independent with quasiparticle excitations which have conical dispersion above and below the Fermi level. Around half filling, the equations of motion for electrons in graphene are equivalent to Weyl equations for massless Dirac fermions giving linear dispersion relations . The electronic system displays hence a relativistic-like invariance at low energies which is at the origin of the finite lower bound in the conductivity, of the absence of backscattering in the presence of long-range scatterers and the Andreev reflection at the graphene-superconductor interfaces. Indeed it is well known that, at the interface between a normal metal and a superconductor, dissipative electrical current is converted into supercurrent, hence without dissipation, by means the Andreev reflection mechanism: an electron, excited slightly above the Fermi level in the normal metal, is back reflected at the interface as a hole, excited slightly below the Fermi level, and the missing charge 2e is removed as Cooper pair in superconducting condensate; this process determines the conductance of the interface at voltages below the superconducting gap. We study the way in which the superconducting correlations are induced in graphene ribbon when it is placed between two superconductors, how such correlations may depend on complex edge structure of the ribbon, on the geometry of the experimental setup and what is the role of Andreev reflection in Josephson effect at superconducting contacts.
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