Properties of superconductor-Luttinger liquid hybrid systems

SummaryIn this contribution we review some properties of a Luttinger liquid (LL) connected to superconducting leads. We first consider the Josephson effect for a LL connected by tunnel junctions to two superconductors. At zero temperature, the critical current is found to decay algebraically with increasing distanced between the junctions. The decay is characterized by an exponent which depends on the strength of the interaction. At finite temperaturesT, lower than the superconducting transition temperatureTc, there is a crossover from algebraic to exponential decay of the critical current as a function ofd, at a distance of the order of ħvF /kBT. Moreover, the dependence of the critical current on temperature shows non-monotonic behaviour. We also consider the frequency and space dependence of the local tunneling density of states of a LL which is connected to a superconductor. This couplingstrongly modifies the single-particle properties of the LL. It significantly enhances the density of states near the Fermi level, whereas this quantity vanishes as a power law for an isolated LL.