Full range of proximity effect probed with Superconductor/Graphene/Superconductor junctions

摘要

The high tunability of the density of states of graphene makes it an idealprobe of quantum transport in different regimes. In particular, thesupercurrent that can flow through a non-superconducting (N) material connectedto two superconducting electrodes, crucially depends on the lenghth of the Nrelative to the superconducting coherence length. Using graphene as the Nmaterial we have investigated the full range of the superconducting proximityeffect, from short to long diffusive junctions. By combining severalS/graphene/S samples with different contacts and lengths, and measuring theirgate-dependent critical currents ($ I_c $) and normal state resistance $ R_N $,we compare the product $eR_NI_c$ to the relevant energies, the Thouless energyin long junctions and the superconducting gap of the contacts in shortjunctions, over three orders of magnitude of Thouless energy. The experimentalvariations strikingly follow a universal law, close to the predictions of theproximity effect both in the long and short junction regime, as well as in thecrossover region, thereby revealing the interplay of the different energyscales. Differences in the numerical coefficients reveal the crucial roleplayed by the interfacial barrier between graphene and the superconductingelectrodes, which reduces the supercurrent in both short and long junctions.Surprisingly the reduction of supercurrent is independent of the gate voltageand of the nature of the electrodes. A reduced induced gap and Thouless energyare extracted, revealing the role played by the dwell time in the barrier inthe short junction, and an effective increased diffusion time in the longjunction. We compare our results to the theoretical predictions of Usadelequations and numerical simulations which better reproduce experiments withimperfect NS interfaces.