Quasi-Andreev reflection in inhomogeneous Luttinger liquids

Reflection of charge excitations at the step in the interaction strength in a Luttinger liquid can be of the Andreev type, even the interactions are purely repulsive. The region with stronger repulsion plays the role of a normal metal in a normal-metal/superconductor junction, whereas the region with weaker repulsion plays the role of a superconductor. It is shown that this quasi-Andreev reflection leads to a number of proximitylike effects, including the local enhancement (suppression) of superconducting fluctuations on the quasinormal (quasisuperconducting) side of the step and significant modification of the local density of states, as well as others. The observable consequences of these proximity effects are analyzed for the case of single- and two-particle tunneling from a normal-metal or superconducting tip into an inhomogeneous Luttinger-liquid wire.