Andreev bound states in high-<i>T</i>_<i>c</i>superconducting junctions

Abstract

The formation of bound states at surfaces of materials with an energy gap in\nthe bulk electron spectrum is a well known physical phenomenon. At\nsuperconductor surfaces, quasiparticles with energies inside the\nsuperconducting gap $\\Delta$ may be trapped in bound states in quantum wells,\nformed by total reflection against the vacuum and total Andreev reflection\nagainst the superconductor. Since an electron reflects as a hole and sends a\nCooper pair into the superconductor, the surface states give rise to resonant\ntransport of quasiparticle and Cooper pair currents, and may be observed in\ntunneling spectra. In superconducting junctions, these surface states may\nhybridize and form bound Andreev states, trapped between the superconducting\nelectrodes. In d-wave superconductors, the order parameter changes sign under\n$90^o$ rotation and, as a consequence, Andreev reflection may lead to the\nformation of zero energy quasiparticle bound states, midgap states (MGS). The\nformation of MGS is a robust feature of d-wave superconductivity and provides a\nunified framework for many important effects which will be reviewed: large\nJosephson current, low-temperature anomaly of the critical Josephson current,\n$\\pi$-junction behavior, $0\\to \\pi$ junction crossover with temperature,\nzero-bias conductance peaks, paramagnetic currents, time reversal symmetry\nbreaking, spontaneous interface currents, and resonance features in subgap\ncurrents. Taken together these effects, when observed in experiments, provide\nproof for d-wave superconductivity in the cuprates.\n