Impurity-induced states in conventional and unconventional superconductors

Abstract

This review presents recent developments in the understanding of how impurities influence the electronic states in the bulk properties of superconductors. The focus is on quasilocalized states in the vicinity of impurity sites in conventional and unconventional superconductors and the goal is to provide a unified framework for their description. The nonmagnetic impurity resonances in unconventional superconductors are directly related to the Yu-Shiba-Rusinov states around magnetic impurities in conventional $s$-wave systems. The physics behind these states, including the quantum phase transition between screened and unscreened impurities, are reviewed and recent work on $d$-wave superconductors is emphasized. The bound states are seen in scanning-tunneling spectroscopy measurements on high-${T}_{c}$ cuprates, which are described in detail. This paper discusses very recent progress in our understanding of states coupled to impurity sites, which have their own dynamics. Also reviewed are inelastic electron-tunneling spectroscopy features that could be seen by scanning-tunneling microscopy in real space and their Fourier-transformed images and impurity resonances in the presence of an order competing with superconductivity. The last part of the review is devoted to the influence of local deviations of the impurity concentration from its average value on the density of states in $s$-wave superconductors. Discussed is how these fluctuations affect the density of states and it is shown that $s$-wave superconductors are, strictly speaking, gapless in the presence of an arbitrarily small concentration of magnetic impurities.