Vortex entanglement in disordered superconductors

Vortex entanglement and pinning in multiply connected disordered superconductors are studied. It is shown that the winding of vortices around repulsive obstacles is greatly enhanced by quenched columnar disorder and suppressed by point disorder, compared to the clean case. This leads to an additional contribution to the effective pinning force acting on vortices, which, unlike the conventional mechanisms of pinning, grows with temperature.     

Quasiparticle conductivities in disordered d-wave superconductors

We study the quasiparticle transport coefficients in disordered d-wave superconductors. We find that spin and charge excitations are generally localized unless magnetic impurities are present. If the system is close to a nesting point in the impurity-scattering unitary limit, the tendency towards localization is reduced while the quasiparticle density of states gets enhanced by disorder. We also show that the residual repulsive interaction among quasiparticles has a delocalizing effect and increases the density of states.     

Flux front penetration in disordered superconductors

We investigate flux front penetration in a disordered type-II superconductor by molecular dynamics simulations of interacting vortices and find scaling laws for the front position and the density profile. The scaling can be understood by performing a coarse graining of the system and writing a disordered nonlinear diffusion equation. Integrating numerically the equation, we observe a crossover from flat to fractal front penetration as the system parameters are varied. The value of the fractal dimension indicates that the invasion process is described by gradient percolation.     

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)].     

Nuclear spin relaxation in strongly disordered superconductors

The influence of nonmagnetic impurity and spin-orbit scattering on the nuclear spin-lattice relaxation rate in strongly disordered superconductors is presented. Using Anderson's exact-eigenstate formalism, it is shown that there exist two effects of disorder onT ₁ ^–1 . Firstly, nonmagnetic impurity and spin-orbit scattering enhances the magnitude of the relaxation rate in the same manner as in the normal dirty metal due to the diffusive nature of quasiparticle motion. Secondly, the Hebel-Slichter peak becomes suppressed due to the disorder enhancement of the quasiparticle inelastic scattering rate due to phonon, Coulomb, and/or spin-fluctuation interactions. Comparison with the available experimental data is made.     

Quantum critical fluctuations in disordered d-wave superconductors

To explain the strong quasiparticle damping in the cuprates, Sachdev and collaborators proposed to couple the system to a critically fluctuating id(xy)- or is-order parameter mode. Here we generalize the approach to the presence of static disorder. In the id case, the order parameter dynamics becomes diffusive, but otherwise much of the phenomenology of the clean case remains intact. In contrast, the interplay of disorder and is-order parameter fluctuations leads to a secondary superconductor transition, with a critical temperature exponentially sensitive to the impurity concentration.     

Quantum Hall effects in layered disordered superconductors

Layered singlet paired superconductors with disorder and broken time reversal symmetry are studied, demonstrating a phase diagram with charge-spin separation in transport. In terms of the average intergrain transmission and the interlayer tunneling we find quantum Hall phases with spin Hall coefficients of sigma(spin)(xy)=0,2 separated by a spin metal phase. We identify a spin metal-insulator localization exponent as well as a spin conductivity exponent of approximately 0.96. In the presence of a Zeeman term an additional sigma(spin)(xy)=1 phase appears.     

Keldysh proximity action for disordered superconductors

We review a novel approach to the superconductive proximity effect in disordered normal-superconducting (N-S) structures. The method is based on the multicharge Keldysh action and is suitable for the treatment of interaction and fluctuation effects. As an application of the formalism, we study the subgap conductance and noise in two-dimensional N-S systems in the presence of the electron-electron interaction in the Cooper channel. It is shown that singular nature of the interaction correction at large scales leads to a nonmonotonuos temperature, voltage and magnetic field dependence of the Andreev conductance.     

Spin and density fluctuations in disordered narrow-band superconductors

A tight-binding theory of strong-coupling superconductivity is formulated on the basis of a random lattice model with local electron-electron and contact-type electronphonon interactions. Functional-derivative technique yields a systematic deduction of the electron self-energy in terms of Coulomb repulsion, density and spin fluctuations. A novel procedure is proposed to average disordered Berk-Schrieffer-type equations. The phonon ( ^ph)-, Coulomb ^C-, and paramagnon ( ^m)-mediated coupling parameters entering the superconductingT _c are calculated for diffusive behaviour in dirty systems or alloys. The critical reduction ofT _c due to ^m differs from the logarithmic singularity for a clean sample.     

Antiferromagnetic order in Pauli-limited unconventional superconductors

We develop a theory of the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in CeCoIn(5). We show that in Pauli-limited nodal superconductors the nesting of the quasiparticle pockets induced by Zeeman pair breaking leads to incommensurate AFM with the magnetic moment normal to the field. We compute the phase diagram and find a first order transition to the normal state at low temperatures, the absence of normal state AFM, and the coexistence of SC and AFM at high fields, in agreement with experiments. We also predict the existence of a new double-Q magnetic phase.     

Heat capacity of disordered and crystalline superconductors

Low temperature heat capacity measurements on disordered and crystalline Nb_0.26Zr_0.74 alloys show that the former has a much larger heat capacity jump (ΔC/γT_c ≈ 2.4) than the latter and that the disorder decreases the superconducting transition temperature (T_c) rather than enhances it.     

Matrix field theory for disordered local pairing superconductors with two glass order parameters and spin-flip pairbreaking processes

We derive the exact matrix field theory for a replicated grassmannian representation of a local pairing superconducting disorder ensemble including three superconducting order parameters and the spin-flip pairbreaking mechanism. Disorder is assumed to be gaussian distributed. We find by exactly solving the saddle-point equation the criterion for a vanishing gap ^–1 + ^–1 , where denotes the averaged superconducting order parameter, ^–1 the spin-flip scattering rate, and ^–1 the scattering rate corresponding to correlations of Re(–). Taken at =0, our field theory, which is exact in all orders of ^–1 , contains new terms in addition to those of theO( ^–1 ) model derived by Efetov et al. Our formulation transfers correctly to all orders the invariances of the action into symmetries of the matrix field theory. The saddle point approximation is outlined and it is shown how singular corrections to the saddle point density of states arise atE _F in a gapless superconductor. Finally singular corrections in the two particle propagator, the density correlation function and the conductivity are calculated for =0 in one loop order. It turns out that these corrections can be entirely expressed by those of the single particle density of states.