Graphene is a 2D crystal made of carbon atoms packed in a honeycomb structure. Ballistic transport in this outstanding material has been demonstrated either in short sample or suspended sample, by means of conductance and shot noise measurements [1-3]. We have probed recently with another powerful method the distribution of transmission eigenmodes in graphene by investigating the supercurrent phase relation (CPR) of a superconductor-graphene-superconductor junction [4]. The supercurrent corresponds to a non-dissipative current which originates from the proximity effect at the superconductor/graphene interface. So far, only switching current measurements in graphene junctions have been reported [5,6]. The CPR measurement allows us to extract the true critical current defined as the maximum of the supercurrent. The experimental setup consists of a graphene junction embedded in an LC tank circuit terminating a 50 Ohm coaxial line. Using reflection measurement of a 700 MHz signal, we have extracted the phase () dependence of the Josephson inductance LJ, and successively deduced the CPR via the relation LJ=0.(dIs/d)-1, where 0 is the flux quantum. At the charge neutrality point (CNP), we find a non-sinusoidal CPR that matches the CPR calculated from Usadel equations for a diffusive, intermediate-length junction. With increasing temperature, we observe a decrease of the non-sinusoidal character of the CPR which agrees with the diffusive calculation. Far away from the CNP, the non-sinusoidal character of the CPR increases linearly with the product RNIC (RN is the normal resistance), reaching close to the ballistic prediction at high charge density, in accordance with an increase of the mean free path governed by screened Coulomb impurities. [1] F. Miao, S. Wijeratne, Y. Zhang, U.C. Coskun, W. Bao, and C.N. Lau, Science 317, 1530 (2007). [2] R. Danneau et al., Phys. Rev. Lett. 100, 196802 (2008); J. Low Temp. Phys. 153, 374 (2008). [3] A.F. Young and P. Kim, Nat. Phys. 5, 222 (2009). [4] A. Fay, M. Wiesner, M.Y. Tomi, P. Lähteenmäki, and P.J. Hakonen, submitted. [5] H.B. Heersche, P. Jarillo-Herrero, J. Oostinga, L.Vandersypen, and A. Morpurgo, Nature 446, 56 (2007). [6] X. Du, I. Skachko, and E. Y. Andrei, Phys. Rev. B 77, 184507 (2008).
Low Temperature Laboratory, Helsinki University (Finland)