PROPERTIES OF SUPERCONDUCTOR-LUTTINGER LIQUID HYBRID SYSTEMS

In this contribution we review some properties of a Luttinger liquid ( LL) connected to superconducting leads. We first consider the Josephso n effect for a LL connected by tunnel junctions to two superconductors . At zero temperature, the critical current is found to decay algebrai cally with increasing distance d between the junctions. The decay is c haracterized by an exponent which depends on the strength of the inter action. At finite temperatures T, lower than the superconducting trans ition temperature T-c, there is a crossover from algebraic to exponent ial decay of the critical current as a function of d, at a distance of the order of hv(F)/k(B) T. Moreover, the dependence of the critical c urrent on temperature shows non-monotonic behaviour. We also consider the frequency and space dependence of the local tunneling density of s tates of a LL which is connected to a superconductor. This coupling st rongly modifies the single-particle properties of the LL. It significa ntly enhances the density of states near the Fer mi level, whereas thi s quantity vanishes as a power law for an isolated LL.