It is shown that weak correlations between the pair-breaking impurities in superconductors influence a temperature dependence of the order parameter within the Ginzburg and Landau region if the correlation radius of impurities R is greater than the coherence length of the superconductor $ξ_0$.Dependence of the square of the average order parameter on a temperature difference $T_c-T$ changes its slope in a region $ξ_0\sqrt{T_c/(T_c-T)\sim R $. Influence of correlations on other thermodynamic properties of superconductors is discussed too.
We calculate frequency and temperature dependence of the anomalous ac Hall conductivity induced by impurity scattering in a chiral px+ipy superconductor, such as Sr2RuO4, with spontaneous time-reversal-symmetry breaking in the absence of an external magnetic field. We consider two models of disorder, Gaussian and non-Gaussian, characterized by the second and third moments of the random impurity potential, respectively. Within both models, we find that the anomalous Hall conductivity has a finite real value at zero frequency, exhibits singularities at the threshold of photon absorption across t…
We generalize Abrikosov-Gor'kov solution of the problem of weakly coupled superconductor with impurities on the case of a multiband superconductor with arbitrary interband order parameter anisotropy, including interband sign reversal of the order parameter. The solution is given in terms of the effective (renormalized) coupling matrix and describes not only $T_c$ suppression but also renormalization of the superconducting gap basically at all temperatures. In many limiting cases we find analytical solutions for the critical temperature suppression. We illustrate our results by numerical calcul…
We study the effect of nonmagnetic impurities on the local density of states (LDOS) in s-wave superconductors. The quasiclassical equations of superconductivity are solved selfconsistently to show how LDOS evolves with impurity concentration. The spatially averaged zero-energy LDOS is a linear function of magnetic induction in low fields, N(E=0)=cB/H_{c2}, for all impurity concentration. The constant of proportionality "c" depends weakly on the electron mean free path. We present numerical data for differential conductance and spatial profile of zero-energy LDOS which can help in estimating th…
Nanocenter CENN（纳米中心CENN）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学物理学院）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）；Department of Physics and Astronomy, Center for Materials Theory, Rutgers University（罗格斯大学物理与天文学系材料理论中心）；Department of Physics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校物理系）；Max-Planck Institute for Solid State Research（马克斯·普朗克固体研究所）
When subject to a weak magnetic impurity distribution, the order parameter and quasi-particle energy gap of a weakly disordered bulk s-wave superconductor are suppressed. In the Born scattering limit, recent investigations have shown that `optimal fluctuations' of the random impurity potential can lead to the nucleation of `domains' of localised states within the gap region predicted by the conventional Abrikosov-Gor'kov mean-field theory, rendering the superconducting system gapless at any finite impurity concentration. By implementing a field theoretic scheme tailored to the weakly disordere…
We study the renormalization of the gap of an s-wave superconductor in the presence of two magnetic impurities. For weakly bound Shiba states, we analytically calculate the part of the gap renormalization that is sensitive to the relative orientation of the two impurity spins. For impurities with a strong exchange coupling to the conduction electrons, we solve the gap equation self-consistently by numerics and find that the sub-gap Shiba state turns into a supra-gap Andreev state when the local gap parameter changes sign under the impurities.
We consider the effect of nonmagnetic and magnetic impurities on the superheating field $H_s$ in a type-II superconductor. We solved the Eilenberger equations, which take into account the nonlinear pairbreaking of Meissner screening currents, and calculated $H_s(T)$ for arbitrary temperatures and impurity concentrations in a single-band s-wave superconductor with a large Ginzburg-Landau parameter. At low temperatures nonmagnetic impurities suppress a weak maximum in $H_s(T)$ which has been predicted for the clean limit, resulting instead in a maximum of $H_s$ as a function of impurity concentr…
High-quality K(Fe$_{1-x}$Co$_x$)$_2$As$_2$ single crystals have been grown by using KAs flux method. Instead of increasing the superconducting transition temperature $T_{\rm c}$ through electron doping, we find that Co impurities rapidly suppress $T_{\rm c}$ down to zero at only $x \approx$ 0.04. Such an effective suppression of $T_{\rm c}$ by impurities is quite different from that observed in Ba$_{0.5}$K$_{0.5}$Fe$_2$As$_2$ with multiple nodeless superconducting gaps. Thermal conductivity measurements in zero field show that the residual linear term $κ_0/T$ only change slightly with $3.4\%$ …
We calculate the anomalous Hall conductance of superconductors with spin-orbit interaction and with either uniform or local magnetization. In the first case we consider a uniform ferromagnetic ordering in a spin triplet superconductor, while in the second case we consider a conventional s-wave spin singlet superconductor with a magnetic impurity (or a diluted set of magnetic impurities). In the latter case we show that the anomalous Hall conductance can be used to track the quantum phase transition, that occurs when the spin coupling between the impurity and electronic spin density exceeds a c…
We demonstrate the formation of robust zero energy modes close to magnetic impurities in the iron-based superconductor FeSe$_{1-x}$Te$_x$. We find that the Zeeman field generated by the impurity favors a spin-triplet inter-orbital pairing as opposed to the spin-singlet intra-orbital pairing prevalent in the bulk. The preferred spin-triplet pairing preserves time-reversal symmetry and is topological, as robust, topologically-protected zero modes emerge at the boundary between regions with different pairing states. Moreover, the zero modes form Kramers doublets that are insensitive to the direct…
We show that, in contrast with the usual electron-phonon Migdal-Eliashberg theory, the critical temperature Tc of an isotropic s-wave nonadiabatic superconductor is strongly reduced by the presence of diluted non-magnetic impurities. Our results suggest that the recently observed Tc-suppression driven by disorder in K3C60 [Phys. Rev. B vol.55, 3866 (1997)] and in Nd(2-x)CexCuO(4-delta) [Phys. Rev. B vol.58, 8800 (1998)] could be explained in terms of a nonadiabatic electron-phonon coupling. Moreover, we predict that the isotope effect on Tc has an impurity dependence qualitatively different fr…
Compensation of the reduction of $T_{c}$ caused by magnetic impurities has been observed as a consequence of radiation damage. Using the recent theory by Kim and Overhauser (KO) we consider the effect of radiation damage on the $T_{c}$ of superconductors having magnetic impurities. We find a good fitting to the experimental data. It is also pointed out that Gor'kov's formalism with the pairing constraint derived from the Anomalous Green's function leads to KO theory.
Weakly disordered superconducting films can be driven into an anomalous low temperature resistive state upon applying a magnetic field. Recent experiments on weakly disordered amorphous InO$_x$ have established that both the Hall resistivity and the frequency of a cyclotron-like resonance in the anomalous metal are highly suppressed relative to the values expected for a conventional metal. We show that both of these observations can be understood from the flux flow dynamics of vortices in a superconductor with significant vortex pinning. Results for flux flow transport are obtained using a sys…
A theory of the local magnetic response of a nonmagnetic impurity in a doped antiferromagnet, as relevant to the normal state in cuprates, is presented. It is based on the assumption of the overdamped collective mode in the bulk system and on the evidence, that equal-time spin correlations are only weakly renormalized in the vicinity of the impurity. The theory relates the Kondo-like behavior of the local susceptibility to the anomalous temperature dependence of the bulk magnetic susceptibility, where the observed increase of the Kondo temperature with doping reflects the crossover to the Ferm…
Tunneling measurements of the temperature dependence of the electronic density of states (DOS) of ultrathin bilayers of Pb and Ag reveal that their superconducting energy gap, $Δ(T)$, evolves similarly to BCS predictions despite the presence of a large anomalous DOS at the Fermi energy that persists as $T\to 0$. The gap ratio, ${2Δ(0)}\over {k_BT_c}$, systematically decreases more than 20% below the BCS universal value of 3.52 in bilayers with the lowest superconducting transition temperatures, $T_c$; a behavior we deem super weakly coupled. A semi-quantitative model suggests that the reduced …
Temperature dependent resistivity of the iron-based superconductor NdFeAsO0.88F0.12 was measured under different applied fields and excitation currents. Arrhenius plot shows an anomalous tail effect, which contains obvious two resistivity dropping stages. The first is caused by the normal superconducting transition, and the second is supposed to be related to the weak-link between the grains. A model for the resistivity dropping related to the weak-link behavior is proposed, which is based on the Josephson junctions formed by the impurities in grain boundaries like FeAs, Sm2O3 and cracks toget…
Chiral superconductors exhibit novel transport properties that depend on the topology of the order parameter, topology of the Fermi surface, the spectrum of bulk and edge Fermionic excitations, and the structure of the impurity potential. In the case of electronic heat transport, impurities induce an anomalous (zero-field) thermal Hall conductivity that is easily orders of magnitude larger than the quantized edge contribution. The effect originates from branch-conversion scattering of Bogoliubov quasiparticles by the chiral order parameter, induced by potential scattering. The former transfers…
Substitutional impurities in the CuO2 planes of the cuprates allow us to probe the electronic properties of the host material. The pseudo-gap in the underdoped regime is unmodified far from the impurities even though Tc is greatly reduced. The spin polarisation induced by magnetic impurities has an oscillatory behaviour reflecting the existing AF correlations between the Cu spins. Its influence on the NMR spectra opens a way to determine the q dependence of the static spin susceptibility and the T dependence of the AF correlation length. NMR measurements demonstrate that non-magnetic impuritie…
The Kondo effect in superconductors is frequently investigated using the local quasiparticle density of states as sole bath characteristics, i.e., the presence of anomalous propagators is ignored. Here we point out that this treatment is exact for a number of situations, including point-like impurities in d-wave superconductors. We comment on recent investigations [M. Matsumoto and M. Koga, J. Phys. Soc. Jpn. 70, 2860 (2001), cond-mat/0011256, and Phys. Rev. B 65, 024508 (2002), cond-mat/0103053] which reached different conclusions: while their numerical results are likely correct, their inter…
The question of anomalous transport due to a band of impurity states in unconventional superconductors is discussed. In general, the bound state energies are not in midgap, even in the unitarity limit. This implies that, generically, the states associated with impurities are broad resonances, not true bound states. There is no impurity band in the usual sense of the phrase. The wavefunctions of these resonances possess interesting anisotropies in real space, but this does not result in anomalous hopping between impurities. I conclude that the system of resonances produces no qualitative modifi…
Recent experimental and theoretical studies have highlighted the possible role of a electronic nematic liquid in underdoped cuprate superconductors. We calculate, within a model of d-wave superconductor with Hubbard correlations, the spin susceptibility in the case of a small explicitly broken rotational symmetry of the underlying lattice. We then exhibit how the induced spin response asymmetry is strongly enhanced by correlations as one approaches the instability to stripe order. In the disorder-induced stripe phase, impurities become spin nematogens with a C_2 symmetric impurity resonance st…
To investigate the validity of the Wiedemann-Franz (WF) law in disordered but metallic cuprates, the low-temperature charge and heat transport properties are carefully studied for a series of impurity-substituted and carrier-overdoped La_{1.8}Sr_{0.2}Cu_{1-z}M_zO_4 (M = Zn or Mg) single crystals. With moderate impurity substitution concentrations of z = 0.049 and 0.082 (M = Zn), the resistivity shows a clear metallic behavior at low temperature and the WF law is confirmed to be valid. With increasing impurity concentration to z = 0.13 (M = Zn) or 0.15 (M = Mg), the resistivity shows a low-T up…
Unlike anomalous quantum Hall insulators, clean single-band chiral superconductors do not exhibit intrinsic Hall effect at the one-loop approximation. Finite ac Hall conductance was found to emerge beyond one-loop, such as with vertex corrections associated with extrinsic random impurity scatterings. In this paper, we investigate the effect of impurities embedded in single-band chiral superconductors in a superlattice pattern, instead of in random distributions. The impurity-induced Bogoliubov quasiparticle bound states hybridize to form subgap bands, constituting an emergent low-energy effect…
