What can Andreev bound states tell us about superconductors?

Zero-energy Andreev bound states, which manifest themselves in the tunnelling spectra as zero-bias conductance peaks (ZBCPs), are abundant at interfaces between superconductors and other materials and on the nodal surface of high-temperature superconductors. In this review, we focus on the information such excitations can provide on the properties of superconductor systems. First, a general introduction to the physics of Andreev bound states in superconductor/normal metal interfaces is given with a particular emphasis on why they appear at zero energy in d-wave superconductors. Then, specific spectroscopic tunnelling studies of thin films, bilayers and junctions are described, focusing on the corresponding ZBCP features. Scanning tunnelling spectroscopy (STS) studies show that the ZBCPs on the c-axis YBa₂Cu₃O_7- (YBCO) films are correlated with the surface morphology and appear only in proximity to (110) facets. STS on c-axis La_1.88Sr_0.12CuO₄ (LSCO) films exhibiting the 1/8 anomaly shows spatially modulated peaks near zero bias associated with the anti-phase ordering of the d-wave order parameter predicted at this doping level. ZBCPs were also found in micrometre-size edge junctions of YBCO/SrRuO₃/YBCO, where SrRuO₃ is ferromagnetic. Here, the results are consistent with a crossed Andreev reflection effect (CARE) at the narrow domain walls of the SrRuO₃ ZBCPs measured in STS studies of manganite/cuprate bilayers could not be attributed to CARE because the manganite's domain wall is much larger than the coherence length in YBCO, and instead are attributed to proximity-induced triplet-pairing superconductivity with non-conventional symmetry. And finally, ZBCPs found in junctions of non-intentionally doped topological insulator films of Bi₂Se₃ and the s-wave superconductor NbN are attributed to proximity-induced p triplet order parameter in the topological material.This article is part of the theme issue 'Andreev bound states'.