Andreev bound states in high-T-c superconducting junctions

The formation of bound states at surfaces of materials with an energy gap i n the bulk electron spectrum is a well known physical phenomenon. At superc onductor surfaces, quasiparticles with energies inside the superconducting gap a may be trapped in bound states in quantum wells, formed by total refl ection against the vacuum and total Andreev reflection against the supercon ductor. Since an electron reflects as a hole and sends a Cooper pair into t he superconductor, the surface states give rise to resonant transport of qu asiparticle and Cooper pair currents, and may be observed in tunnelling spe ctra. In superconducting junctions these surface states may hybridize and f orm bound Andreev states, trapped between the superconducting electrodes. I n d-wave superconductors, the order parameter changes sign under 90 degrees rotation and, as a consequence, Andreev reflection may lead to the formati on of zero energy quasiparticle bound states, midgap states (MGS). The form ation of MGS is a robust feature of d-wave superconductivity and provides a unified framework for many important effects which will be reviewed: large Josephson current, low-temperature anomaly of the critical Josephson curre nt, pi -junction behaviour, 0 --> pi junction crossover with temperature, z ero-bias conductance peaks, paramagnetic currents, time reversal symmetry b reaking, spontaneous interface currents, and resonance features in subgap c urrents. Taken together these effects, when observed in experiments, provid e proof for d-wave superconductivity in the cuprates.