Andreev bound states in dirty unconventional superconductor junctions

We review the recent development in the theory of proximity effect in unconventional superconductor junctions. The low energy transport in the unconventional superconductor junction is governed by two interference effects of a quasiparticle: formation of a midgap Andreev resonant state (MARS) at the junction interface and the diffusion of Cooper pair into a normal-metal (proximity effect). Both of them are sensitive to the pairing symmetry of superconductivity. In a p-wave superconductor junction, the MARS penetrates from a superconductor into a normal-metal and drastically increases the conductance and the Josephson current. We will show that such anomalous quantum transport is the result of a cooperative effect between the MARS and the proximity effect. Experimental trials to detect the Josephson current between two p-wave superconductors are in progress.