Impurity-induced virtual bound states in d-wave superconductors

Emergent normal fluid in the superconducting ground state of overdoped cuprates

The microscopic mechanism for the disappearance of superconductivity in overdoped cuprates is still under heated debate. Here we use scanning tunneling spectroscopy to investigate the evolution of quasiparticle interference phenomenon in Bi2Sr2CuO6+δ over a wide range of hole densities. We find that when the system enters the overdoped regime, a peculiar quasiparticle interference wavevector with arc-like pattern starts to emerge even at zero bias, and its intensity grows with increasing doping level. Its energy dispersion is incompatible with the octet model for d-wave superconductivity, but is highly consistent with the scattering interference of gapless normal carriers. The gapless quasiparticles are mainly located near the antinodes and are independent of temperature, consistent with the disorder scattering mechanism. We propose that a branch of normal fluid emerges from the pair-breaking scattering between flat antinodal bands in the quantum ground state, which is the primary cause for the reduction of superfluid density and suppression of superconductivity in overdoped cuprates.

Josephson Scanning Tunneling Spectroscopy in d_{x^{2}-y^{2}}-Wave Superconductors: A Probe for the Nature of the Pseudogap in the Cuprate Superconductors

Recent advances in the development of Josephson scanning tunneling spectroscopy (JSTS) have opened a new path for the exploration of unconventional superconductors. We demonstrate that the critical current I_{c}, measured via JSTS, images the spatial form of the superconducting order parameter in d_{x^{2}-y^{2}}-wave superconductors around defects and in the Fulde-Ferrell-Larkin-Ovchinnikov state. Moreover, we show that I_{c} probes the existence of phase-incoherent superconducting correlations in the pseudogap region of the cuprate superconductors, thus providing unprecedented insight into its elusive nature. These results provide the missing theoretical link between the experimentally measured I_{c} and the spatial structure of the superconducting order parameter.

Impurity bound states in fully gapped d-wave superconductors with subdominant order parameters

Impurities in superconductors and their induced bound states are important both for engineering novel states such as Majorana zero-energy modes and for probing bulk properties of the superconducting state. The high-temperature cuprates offer a clear advantage in a much larger superconducting order parameter, but the nodal energy spectrum of a pure d-wave superconductor only allows virtual bound states. Fully gapped d-wave superconducting states have, however, been proposed in several cuprate systems thanks to subdominant order parameters producing d + is- or d + id'-wave superconducting states. Here we study both magnetic and potential impurities in these fully gapped d-wave superconductors. Using analytical T-matrix and complementary numerical tight-binding lattice calculations, we show that magnetic and potential impurities behave fundamentally different in d + is- and d + id'-wave superconductors. In a d + is-wave superconductor, there are no bound states for potential impurities, while a magnetic impurity produces one pair of bound states, with a zero-energy level crossing at a finite scattering strength. On the other hand, a d + id'-wave symmetry always gives rise to two pairs of bound states and only produce a reachable zero-energy level crossing if the normal state has a strong particle-hole asymmetry.

Enhanced antiferromagnetic exchange between magnetic impurities in a superconducting host

It is generally believed that superconductivity only weakly affects the indirect exchange between magnetic impurities. If the distance r between impurities is smaller than the superconducting coherence length (r ≲ ξ), this exchange is thought to be dominated by Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions, identical to the those in a normal metallic host. This perception is based on a perturbative treatment of the exchange interaction. Here, we provide a nonperturbative analysis and demonstrate that the presence of Yu-Shiba-Rusinov bound states induces a strong 1/r(2) antiferromagnetic interaction that can dominate over conventional RKKY even at distances significantly smaller than the coherence length (r ≪ ξ). Experimental signatures, implications, and applications are discussed.

Doping dependence of the nonmagnetic impurity resonance in cuprate superconductors

Motivated by the observation that the nonmagnetic impurity induced resonance strength is reduced with underdoping in Bi(2)Sr(2)Ca(Cu(1-y)Zn(y))(2)O(8+x), we study the doping dependence of the nonmagnetic impurity induced resonance in cuprates from the viewpoint of resonating valence bond (RVB) spin liquid theory. It is revealed that the pseudogap state in the Yang, Rice and Zhang ansatz (Yang et al 2006 Phys. Rev. B 73 174501; Rice et al 2012 Rep. Prog. Phys. 75 016502) does not support an impurity resonance state due to the overdamping of the quasiparticle. In the coexistence of the d-wave superconductivity and the RVB gap, our theory provides an alternative but consistent explanation for the reduction of the resonance strength with underdoping, as well as the absence of the resonance in the large gap region.

Impurity-induced bound states and proximity effect in a bilayer exciton condensate

The effect of impurities which induce local interlayer tunneling in bilayer exciton condensates is discussed. We show that a localized single-fermion bound state emerges inside the gap for any strength of impurity scattering and calculate the dependence of the impurity state energy and wave function on the potential strength. We show that such an impurity-induced single-fermion state enhances the interlayer coherence around it, and is similar to the superconducting proximity effect. As a direct consequence of these single-impurity states, we predict that a finite concentration of such impurities will increase the critical temperature for exciton condensation.

Pairing symmetry in a two-orbital exchange coupling model of oxypnictides

We study the pairing symmetry of a two-orbital J1-J2 model for FeAs layers in oxypnictides. We show that the mixture of an intraorbital unconventional s_{x;{2}y;{2}} approximately cos(k_{x})cos(k_{y}) pairing symmetry, which changes sign between the electron and hole Fermi surfaces, and a very small d_{x;{2}-y;{2}} approximately cos(k_{x})-cos(k_{y}) component is favored in a large part of the J1-J2 phase diagram. A pure s_{x;{2}y;{2}} pairing state is favored for J2>J1. The signs of the d_{x;{2}-y;{2}} order parameters in the two different orbitals are opposite. While a small d_{xy} approximately sin(k_{x})sin(k_{y}) interorbital pairing coexists in the above phases, the intraorbital d_{xy} pairing is not favored even for large J2.

Andreev states near short-ranged pairing potential impurities

We study Andreev states near atomic scale modulations in the pairing potential in both s- and d-wave superconductors with short coherence lengths. For a moderate reduction of the local gap, the states exist only close to the gap edge. If one allows for local sign changes of the order parameter, however, resonances can occur at energies close to the Fermi level. The local density of states (LDOS) around such pairing potential defects strongly resembles the patterns observed by tunneling measurements around Zn impurities in Bi2Sr2CaCu2O8+x (BSCCO). We discuss how this phase impurity model of the Zn LDOS pattern can be distinguished from other proposals experimentally.

Low-temperature thermal conductivity of superconductors with gap nodes

We report a detailed analytic and numerical study of electronic thermal conductivity in d-wave superconductors. We compare theory of the crossover at low temperatures from T dependence to T(3) dependence for increasing temperature with recent experiments on YBa(2)Cu(3)O(7) in zero magnetic field for T approximately [0.04 K,0.4 K] by Hill et al. [Phys. Rev. Lett. 92, 027001 (2004)]. Transport theory, including impurity scattering and inelastic scattering within strong-coupling superconductivity, can consistently fit the temperature dependence of the data in the lower half of the temperature regime. We discuss the conditions under which we expect power-law dependences over wide temperature intervals.

Effects of a collective spin resonance mode on the scanning tunneling microscopy spectra of d-wave superconductors

A high-energy spin resonance mode is known to exist in many high-temperature superconductors. Motivated by recent scanning tunneling microscopy experiments in superconducting Bi(2)Sr(2)CaCu(2)O(8+delta), we study the effects of this resonance mode on the local density of states (LDOS). The coupling between the electrons in a d-wave superconductor and the resonance mode produces high-energy peaks in the LDOS, which displays a two-unit-cell periodic modulation around a nonmagnetic impurity. This suggests a new means to not only detect the dynamical spin collective mode but also study its coupling to electronic excitations.

Elasticity-driven nanoscale electronic structure in superconductors

The effects of long-range anisotropic elastic deformations on electronic structure in superconductors are analyzed within the framework of the Bogoliubov-de Gennes equations. Cases of twin boundaries and isolated defects are considered as illustrations. We find that the superconducting order parameter is depressed in the regions where pronounced lattice-deformation occurs. The calculated local density of states suggests that the electronic structure is strongly modulated in response to lattice deformations, and propagates to longer distances. In particular, this allows the trapping of low-lying quasiparticle states around defects. Some of our predictions can be directly tested by scanning tunneling microscopy experiments.

Impurities and quantum interference in the chains of YBa2Cu3O6+x

Motivated by recent experiments, we study the electronic structure near impurities in the chains of YBa2Cu3O6+x. Using a model of proximity induced chain superconductivity, we show that a resonance state in the chain density of states is induced only by a magnetic impurity. The spatial form of the resonance reflects the particle-hole nature of chain superconductivity and therefore distinguishes it from other broken symmetry phases. Because of quantum interference effects between impurities, the chains can undergo a quantum phase transition into a polarized state.

Impurity bound states in disordered d-wave superconductors

Recent STM experiments on Bi2Sr2Ca2Cu3O10 observed sharp bound states associated with Zn and Ni impurities, as previously predicted theoretically. Here we extend the theory to the case of a finite concentration of impurities. Using the nonlocal coherent potential approximation, we show that the resonance peak both broadens and shifts as a function of impurity concentration.

Resonant impurity states in the d-density-wave phase

We study the electronic structure near impurities in the d-density-wave (DDW) state, a possible candidate phase for the pseudogap region of the high-temperature superconductors. We show that the density of states near a nonmagnetic impurity in the DDW state is qualitatively different from that in a superconductor with dx(2)(-y(2)) symmetry. Thus, the electronic structure near impurities can provide insight into the nature of the two phases recently observed by scanning tunneling microscopy experiments in the superconducting state of underdoped Bi-2212 compounds.

Strongly correlated s-wave superconductivity in the N-type infinite-layer cuprate

Quasiparticle tunneling spectra of the electron-doped ( n-type) infinite-layer cuprate Sr0.9La0.1CuO2 reveal characteristics that counter a number of common phenomena in the hole-doped ( p-type) cuprates. The optimally doped Sr0.9La0.1CuO2 with T(c) = 43 K exhibits a momentum-independent superconducting gap Delta = 13.0+/-1.0 meV that substantially exceeds the BCS value, and the spectral characteristics indicate insignificant quasiparticle damping by spin fluctuations and the absence of pseudogap. The response to quantum impurities in the Cu sites also differs fundamentally from that of the p-type cuprates with d(x(2)-y(2))-wave pairing symmetry.

Universal heat transport in Sr2RuO4

We present the temperature dependence of the thermal conductivity kappa(T) of the unconventional superconductor Sr2RuO4 down to low temperatures ( approximately 100 mK). In the T-->0 K limit we found a finite residual term in kappa/T, providing clear evidence for the superconducting state with an unconventional pairing. The residual term remains unchanged for samples with different T(c), demonstrating the universal character of heat transport in this spin-triplet superconductor. The low-temperature behavior of kappa suggests the strong impurity scattering with a phase shift close to pi/2. A criterion for the observation of universality is experimentally deduced.

Impurity states and interlayer tunneling in high temperature superconductors

We argue that the scanning tunneling microscope (STM) images of resonant states generated by doping Zn or Ni impurities into Cu-O planes of BSCCO are the result of quantum interference of the impurity signal coming from several distinct paths. The impurity image seen on the surface is greatly affected by interlayer tunneling matrix elements. We find that the optimal tunneling path between the STM tip and the metal (Cu, Zn, or Ni) d(x(2)-y(2)) orbitals in the Cu-O plane involves intermediate excited states. This tunneling path leads to the fourfold nonlocal filter of the impurity state in Cu-O plane that explains the experimental impurity spectra. Applications of the tunneling filter to the Cu vacancy defects and "direct" tunneling into Cu-O planes are also discussed.

Nanoscale one-dimensional scattering resonances in the CuO chains of YBa(2)Cu(3)O(6+x)

We present scanning tunneling spectroscopy measurements of the CuO chain plane in YBa(2)Cu(3)O(6+x), showing an approximately 25 meV gap in the local density of states (LDOS) filled by numerous intragap resonances: intense peaks in LDOS spectra associated with one-dimensional, Friedel-like oscillations. We discuss how these phenomena shed light on recent results from other probes, as well as their implications for phenomena in the superconducting CuO(2) plane.

Mechanism of pseudogap probed by a local impurity

The response to a local strong nonmagnetic impurity in the pseudogap phase is examined in two distinctly different scenarios: phase fluctuation (PF) of pairing field and d-density-wave (DDW) order. In the PF scenario, the resonance state is generally double peaked near the Fermi level, and is abruptly broadened by vortex fluctuations slightly above the transition temperature. In the DDW scenario, the resonance is single peaked and remains sharp up to gradual intrinsic thermal broadening, and the resonance energy is analytically determined to be at minus of the chemical potential.

Quasiparticle states around a nonmagnetic impurity in a d-density-wave state of high-T(c) cuprates

The electronic structure around a single nonmagnetic impurity in the d-density-wave (DDW) ordering is studied. It is found that a single subgap resonance peak appears in the local density of states around the impurity. In the unitary limit, the position of this resonance peak shifts away from the Fermi energy in accord with the chemical potential. This result is dramatically different from the case of the pure superconducting state for which the impurity resonant energy is approximately pinned at the Fermi level. This can be used to probe the existence of the DDW ordering in cuprates.

Doping and magnetic field dependence of in-plane tunneling into YBa(2)Cu(3)O(7-x): possible evidence for the existence of a quantum critical point

We present tunneling measurements into (1,1,0) YBa(2)Cu(3)O(7-x) films at various doping levels around the optimum. We find that, above a certain doping level near optimum doping, a spontaneous zero bias conductance peak splitting, delta, appears. It increases with doping. It also increases with magnetic field applied along the c axis, for both underdoped and overdoped films. The low field susceptibility chi = d delta /dH/(H-->0) is maximum, possibly diverging when the spontaneous value of delta goes to zero. These results suggest a transition from a pure d(x(2)-y(2)) to a d+id(xy) or d+is order parameter.

Evidence of doping-dependent pairing symmetry in cuprate superconductors

Scanning tunneling spectroscopy studies reveal long-range spatial homogeneity and predominantly d(x(2)-y(2))-pairing spectral characteristics in under- and optimally doped YBa2Cu 3O (7-delta) superconductors, whereas STS on YBa2(Cu 0.9934Zn 0.0026Mg (0.004))3O (6.9) exhibits microscopic spatial modulations and strong scattering near the Zn or Mg impurity sites, together with global suppression of the pairing potential. In contrast, in overdoped (Y 0.7Ca (0.3))Ba 2Cu 3O (7-delta), (d(x(2)-y(2))+s)-pairing symmetry is found, suggesting significant changes in the superconducting ground state at a critical doping value.

Interplay of magnetism and high-Tc superconductivity at individual Ni impurity atoms in Bi2Sr2CaCu2O8+delta

Magnetic interactions and magnetic impurities are destructive to superconductivity in conventional superconductors. By contrast, in some unconventional macroscopic quantum systems (such as superfluid 3He and superconducting UGe2), the superconductivity (or superfluidity) is actually mediated by magnetic interactions. A magnetic mechanism has also been proposed for high-temperature superconductivity. Within this context, the fact that magnetic Ni impurity atoms have a weaker effect on superconductivity than non-magnetic Zn atoms in the high-Tc superconductors has been put forward as evidence supporting a magnetic mechanism. Here we use scanning tunnelling microscopy to determine directly the influence of individual Ni atoms on the local electronic structure of Bi2Sr2CaCu2O8+delta. At each Ni site we observe two d-wave impurity states of apparently opposite spin polarization, whose existence indicates that Ni retains a magnetic moment in the superconducting state. However, analysis of the impurity-state energies shows that quasiparticle scattering at Ni is predominantly non-magnetic. Furthermore, we show that the superconducting energy gap and correlations are unimpaired at Ni. This is in strong contrast to the effects of non-magnetic Zn impurities, which locally destroy superconductivity. These results are consistent with predictions for impurity atom phenomena derived from a magnetic mechanism.

Interacting random Dirac fermions in superconducting cuprates

We study the effects of quasiparticle interactions on disorder-induced localization of Dirac-like nodal excitations in superconducting high- Tc cuprates. As suggested by the experimental angle-resolved photoemission spectroscopy and terahertz conductivity data in Bi2Sr2CaCu2O(8+delta), we focus on the interactions mediated by the order parameter fluctuations near an incipient second pairing transition d --> d + is(id'). We find interaction corrections to the density of states, specific heat, and conductivity as well as phase and energy relaxation rates and assess the applicability of the recent localization scenarios for noninteracting random Dirac fermions to the cuprates.

Marginal Fermi liquid resonance induced by a quantum magnetic impurity in d-wave superconductors

We consider a model of an Anderson impurity embedded in a d(x(2)-y(2))--wave superconducting state to describe the low-energy excitations of cuprate superconductors doped with a small amount of magnetic impurities. Because of the Dirac-like energy dispersion, a sharp localized resonance above the Fermi energy, showing a marginal Fermi liquid behavior ( omega ln omega as omega-->0), is predicted for the impurity states. The same logarithmic dependence of self-energy and a linear frequency dependence of the relaxation rate are also derived for the conduction electrons, characterizing a new universality class for the strong coupling fixed point. At the resonant energies, the spatial distribution of the electron density of states around the magnetic impurity is also calculated.

Impurity in a d-wave superconductor: Kondo effect and STM spectra

We present a theory for recent STM studies of Zn impurities in the superconductor Bi2Sr2CaCu2O8+delta, using insights from NMR experiments which show that there is a net S = 1/2 moment on the Cu ions near the Zn. We argue that the Kondo spin dynamics of this moment is the origin of the low bias peak in the differential conductance, rather than a resonance in a purely potential scattering model. The spatial and energy dependence of the STM spectra of our model can also fit the experiments.

Quasiparticle localization in disordered d-wave superconductors

An extensive numerical study is reported on the disorder effect in two-dimensional d-wave superconductors with random impurities in the unitary limit. It is found that a sharp resonant peak shows up in the density of states at zero energy and correspondingly the finite-size spin conductance is strongly enhanced which results in a nonuniversal feature in one-parameter scaling. However, all quasiparticle states remain localized, indicating that the resonant density peak alone is not sufficient to induce delocalization. In the weak disorder limit, the localization length is so long that the spin conductance at small sample size is close to the universal value predicted by Lee [Phys. Rev. Lett. 71, 1887 (1993)].

Absence of residual quasiparticle conductivity in the underdoped cuprate YBa2Cu4O8

We report measurements of the in-plane thermal conductivity kappa of the stoichiometric underdoped cuprate YBa2Cu4O8 (Y124) below 1 K. kappa(T) is shown to follow a simple phononic T3 dependence at the lowest temperature T for both current directions, with a negligible linear quasiparticle contribution. This observation is in marked contrast with behavior reported in optimally doped cuprates, and implies that extended zero-energy (or low-energy) quasiparticles are absent in Y124.

Details of disorder matter in 2D d-wave superconductors

Within numerically exact solutions of the Bogoliubov-de Gennes equations, we demonstrate that discrepancies between predicted low-energy quasiparticle properties in disordered 2D d-wave superconductors occur because of the unanticipated importance of disorder model details and normal state particle-hole symmetry. For the realistic case, which is best described by a binary alloy model without particle-hole symmetry, we predict density-of-state suppression below an energy scale which appears to be correlated with the corresponding single impurity resonance.

Gap inhomogeneities and the density of states in disordered d-wave superconductors

We report on a numerical study of disorder effects in 2D d-wave BCS superconductors. We compare exact numerical solutions of the Bogoliubov-de Gennes (BdG) equations for the density of states rho(E) with the standard T-matrix approximation. Local suppression of the order parameter near impurity sites, which occurs in self-consistent solutions of the BdG equations, leads to apparent power-law behavior rho(E) approximately |E|(alpha) with nonuniversal alpha over an energy scale comparable to the single-impurity resonance energy Omega(0). We show that the novel effects arise from static spatial correlations between the order parameter and the impurity distribution.

Local density of states around a magnetic impurity in high- T(c) superconductors based on the t-J model

The local density of states (LDOS) around a magnetic impurity in high- T(c) superconductors is studied using the two-dimensional t-J model with a realistic band structure. The order parameters are determined in a self-consistent way within the Gutzwiller approximation and the Bogoliubov-de Gennes theory. In sharp contrast with the nonmagnetic impurity case, the LDOS near the magnetic impurity shows two resonance peaks reflecting the presence of spin-dependent resonance states. It is also shown that these resonance states are approximately localized around the impurity. The present results have an immediate connection with the scanning tunneling spectroscopy observation of Bi2Sr2Ca(Cu1-xNi[Zn](x))(2)O(8+delta).

Imaging the effects of individual zinc impurity atoms on superconductivity in Bi2Sr2CaCu2O8+delta

Although the crystal structures of the copper oxide high-temperature superconductors are complex and diverse, they all contain some crystal planes consisting of only copper and oxygen atoms in a square lattice: superconductivity is believed to originate from strongly interacting electrons in these CuO2 planes. Substituting a single impurity atom for a copper atom strongly perturbs the surrounding electronic environment and can therefore be used to probe high-temperature superconductivity at the atomic scale. This has provided the motivation for several experimental and theoretical studies. Scanning tunnelling microscopy (STM) is an ideal technique for the study of such effects at the atomic scale, as it has been used very successfully to probe individual impurity atoms in several other systems. Here we use STM to investigate the effects of individual zinc impurity atoms in the high-temperature superconductor Bi2Sr2CaCu2O8+delta. We find intense quasiparticle scattering resonances at the Zn sites, coincident with strong suppression of superconductivity within approximately 15 A of the scattering sites. Imaging of the spatial dependence of the quasiparticle density of states in the vicinity of the impurity atoms reveals the long-sought four-fold symmetric quasiparticle 'cloud' aligned with the nodes of the d-wave superconducting gap which is believed to characterize superconductivity in these materials.