We review recent developments in our understanding of how impurities influence the electronic states in the bulk of superconductors. Our focus is on the quasi-localized states in the vicinity of impurity sites in conventional and unconventional superconductors and our goal is to provide a unified framework for their description. The non-magnetic impurity resonances in unconventional superconductors are directly related to the Yu-Shiba-Rusinov states around magnetic impurities in conventional s-wave systems. We review the physics behind these states, including quantum phase transition between screened and unscreened impurity, and emphasize recent work on d-wave superconductors. The bound states are most spectacularly seen in scanning tunneling spectroscopy measurements on high-$T_c$ cuprates, which we describe in detail. We also discuss very recent progress on the states coupled to impurity sites which have their own dynamics, and impurity resonances in the presence of an order competing with superconductivity. Last part of the review is devoted to influence of local deviations of the impurity concentration from its average value on the density of states in s-wave superconductors. We review how these fluctuations affect the density of states and show that s-wave superconductors are, strictly speaking, gapless in the presence of an arbitrarily small concentration of magnetic impurities.

Impurity-induced states in conventional and unconventional superconductors

Superconductivity — one of the best understood many-body problems in physics — has again become a challenge following the discovery of unconventional superconducting materials: these include heavy-fermion1, organic2 and the high-transition-temperature copper oxide3 superconductors In conventional superconductors, the electrons form superconducting Cooper pairs in a spin-singlet state, which has zero total spin (S = 0) In principle, Cooper pairs can also form in a spin-triplet state (S = 1), analogous to the spin-triplet ‘p-wave’ state of paired neutral fermions in superfluid 3He (ref 4) At present, the heavy-fermion compound UPt3 is the only known spin-triplet superconductor5,6, although the layered oxide superconductor Sr2RuO4 (ref 7) is believed, on theoretical grounds8, to be a promising candidate The most direct means of identifying the spin state of Cooper pairs is from measurements of their spin susceptibility, which can be determined by the Knight shift (as probed by nuclear magnetic resonance (NMR)) Here we report Knight-shift measurements of Sr2RuO2 using 17O NMR Our results show no change in spin susceptibility on passing through the superconducting transition temperature, which provides the definitive identification of Sr2RuO4 as a spin-triplet superconductor

Spin-triplet superconductivity in Sr2RuO4 identified by 17O knight shift

The case for dx2 − y2 pairing in the cuprate superconductors

In materials with strong local Coulomb interactions, simple defects such as atomic substitutions strongly affect both macroscopic and local properties of the system. A nonmagnetic impurity, for instance, is seen to induce magnetism nearby. Even without disorder, models of such correlated systems are generally not soluble in 2 or 3 dimensions, and so few exact results are known for the properties of such impurities. Nevertheless, some simple physical ideas have emerged from experiments and approximate theories. Here, we first review what we can learn about this problem from 1D antiferromagnetically correlated systems. We then discuss experiments on the high Tc cuprate normal state which probe the effect of impurities on local charge and spin degrees of freedom, and compare with theories of single impurities in correlated hosts, as well as phenomenological effective Kondo descriptions. Subsequently, we review theories of impurities in d-wave superconductors including residual quasiparticle interactions, and compare with experiments in the superconducting state. We argue that existing data exhibit a remarkable similarity to impurity-induced magnetism in the 1D case, implying the importance of electronic correlations for the understanding of these phenomena, and suggesting that impurities may provide excellent probes of the still poorly understood ground state of the cuprates.

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Defects in correlated metals and superconductors

We report on a study of the electromagnetic response of three different families of high- superconductors that in combination allowed us to cover the whole doping range from under- to overdoped. The discussion is focused on the ab-plane charge dynamics in the pseudogap state which is realized in underdoped materials below a characteristic temperature , a temperature that can significantly exceed the superconducting transition temperature . We explore the evolution of the pseudogap response by changing the doping level, by varying the temperature from above to below , or by introducing impurities in the underdoped compounds. We employ a memory function analysis of the ab-plane optical data that allows us to observe the effect of the pseudogap most clearly. We compare the infrared data with other experimental results, including the c-axis optical response, dc transport, and angle-resolved photoemission.

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The pseudogap state in high- superconductors: an infrared study

The normal and superconducting properties in impurity-doped YBa 2 (Cu 1- x M x ) 3 O 7 (M=Zn and Ni) have been investigated by 63 Cu NMR and NQR techniques. The nonmagnetic Zn-doping into the CuO 2 plane in YBa 2 Cu 3 O 7 (YBCO 7 ) causes a local collapse of antiferromagnetic (AF) spin correlation near Zn impurities and induces a gapless superconductivity with a finite density of states at the Fermi surface. On the other hand, in the case of Ni doping, there is no appreciable modification except for a small decrease of T c , although the Ni spins behave actually as local moments. The gapless feature in Zn-doped YBCO 7 is shown to be consistently interpreted within the framework of the d -wave model with gap zeros of lines at the Fermi surface as argued in heavy fermion superconductors. It is pointed out that the AF spin fluctuation-induced superconductivity is applicable to high- T c cuprates.

Cu NMR and NQR Studies of Impurities-Doped YBa2(Cu1-xMx)3O7 (M=Zn and Ni)

The superconducting property in impurity-doped YBa 2 (Cu 1− x M x ) 3 O 7 (M=Zn and Ni) has been investigated by measuring the nuclear spin-lattice relaxation time T 1 and the Knight shift of 63 Cu in the CuO 2 plane. We have found that Zn doping into the CuO 2 plane in YBa 2 Cu 3 O 7 causes gapless superconductivity at low T , giving rise to a finite density of states at the Fermi surface, while magnetic Ni doping into the CuO 2 plane reduces T c moderately, although Ni spins behave as local moments. The gapless feature in Zn-doped YBCo 7 can be consistently interpreted in the framework of the d-wave model with gap zeros of lines at the Fermi surface, as argued for heavy-fermion superconductors.

J. R. Cooper

Papers

Cu NMR and NQR Studies of Impurities-Doped YBa2(Cu1-xMx)3O7 (M=Zn and Ni)

Cu NMR and NQR study of impurity-doped YBa2Cu3O7