Anomalous proximity effect in d-wave superconductors

The anomalous proximity effect between a d-wave superconductor and a thin disordered normal layer is studied theoretically in the framework of Eilenberger equations. It is shown that disorder of the quasiparticle reflection from this thin layer leads to the formation of an s-wave component localized near the boundary. The angular and spatial structure of the pair potential near the interface is studied. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 478–483 (10 April 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Superflow in d-wave superconductors

Superflow in a phenomenological tight-binding model for the superconducting state of some high-temperature superconductors is discussed thoroughly. The formalism used is explicitly gauge invariant and currents are computed exactly within the BCS theory, going therefore beyond linear response theory. The dependence of gap functions, current density, critical currents and free energy as a function of the superfluid velocity for different angles and doping concentrations is investigated. Different sources of anisotropy, like the dispersion relation of the model, the internal symmetry of the order parameter, and orthorhombic distortions of the lattice are also studied.     

Fractional ac Josephson effect in p- and d-wave superconductors

For certain orientations of Josephson junctions between two p_x-wave or two d-wave superconductors, the subgap Andreev bound states produce a -periodic relation between the Josephson current I and the phase difference : . Consequently, the ac Josephson current has the fractional frequency , where V is the dc voltage. In the tunneling limit, the Josephson current is proportional to the first power (not square) of the electron tunneling amplitude. Thus, the Josephson current between unconventional superconductors is carried by single electrons, rather than by Cooper pairs. The fractional ac Josephson effect can be observed experimentally by measuring frequency spectrum of microwave radiation from the junction. We also study junctions between singlet s-wave and triplet p_x-wave, as well as between chiral -wave superconductors.Received: 24 September 2003, Published online: 2 April 2004PACS: 74.50. + r Tunneling phenomena; point contacts, weak links, Josephson effects - 74.70.Kn Organic superconductors - 74.72.-h Cuprate superconductors (high-T_c and insulating parent compounds) - 74.70.Pq Ruthenates     

Zinc impurities in d-wave superconductors

We study the two-dimensional Hubbard model with nonmagnetic Zn impurities modeled by binary diagonal disorder using quantum Monte Carlo within the dynamical cluster approximation. With increasing Zn content we find a strong suppression of d-wave superconductivity and an enhancement of antiferromagnetic spin correlations. T(c) vanishes linearly with Zn impurity concentration. The spin susceptibility changes from pseudogap to Curie-Weiss-like behavior indicating the existence of free magnetic moments in the Zn doped system. We interpret these results within the resonating-valence-bond picture.     

Surface electron scattering in d-wave superconductors

A theoretical model of a rough surface in a d-wave superconductor is studied for the general case of arbitrary strength of electron scattering by an impurity layer covering the surface. Boundary conditions for quasiclassical Eilenberger equations are derived at the interface between the impurity layer and the d-wave superconductor. The model is applied to the self-consistent calculation of the surface density of states and the critical current in d-wave Josephson junctions. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 242–246 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

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)].     

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.     

Quantum phase transitions in d-wave superconductors

Motivated by the strong, low temperature damping of nodal quasiparticles observed in some cuprate superconductors, we study quantum phase transitions in d(x(2)-y(2)) superconductors with a spin-singlet, zero momentum, fermion bilinear order parameter. We present a complete, group-theoretic classification of such transitions into seven distinct cases (including cases with nematic order) and analyze fluctuations by the renormalization group. We find that only two, the transitions to d(x(2)-y(2))+is and d(x(2)-y(2))+id(xy) pairing, possess stable fixed points with universal damping of nodal quasiparticles; the latter leaves the gapped quasiparticles along (1,0), (0,1) essentially undamped.     

Thermal fluctuations in d-wave layered superconductors

We study the thermal fluctuations of anisotropic order parameters (OP) in layered superconductors. In particular, for copper oxides and a d-wave OP, we present some experimental consequences of fluctuations in the direction normal to the layers. It is shown that the c-axis penetration depth λ_c can have a “disorder-like” quadratic temperature dependence at low temperature. The fluctuations are analyzed in the framework of a Lawrence-Doniach model with an isotropic Fermi surface. Anisotropies pin the orientation of the OP to the crystallographic axes of the lattice. Then we study an extended t-J model that fits Fermi surface data of bilayers YBCO and BSCCO. This leads to a d-wave OP with two possible orientations and, including the thermal fluctuations, yields the announced temperature dependence of λ_c. Furthermore a reservoir layer is introduced. It implies a finite density of states at the Fermi energy which is successfully compared to conductance and specific heat measurements.     

Disordered d-wave superconductors with interactions

We study the localization properties of disordered d-wave superconductors by means of the fermionic replica trick method. We derive the effective non-linear σ-model describing the diffusive modes related to spin transport which we analyze by the Wilson–Polyakov renormalization group. A lot of different symmetry classes are considered within the same framework. According to the presence or the absence of certain symmetries, we provide a detailed classification for the behavior of some physical quantities, like the density of states, the spin and the quasiparticle charge conductivities. Following the original Finkel'stein approach, we finally extend the effective functional method to include residual quasiparticle interactions, at all orders in the scattering amplitudes. We consider both the superconducting and the normal phase, with and without chiral symmetry, which occurs in the so-called two-sublattice models.     

Phase fluctuations in strongly coupled d-wave superconductors

We present a numerically exact solution for the BCS Hamiltonian at any temperature, including the degrees of freedom associated with classical phase, as well as amplitude fluctuations via a Monte Carlo integration. This allows for an investigation over the whole range of couplings: from weak attraction, as in the well-known BCS limit, to the mainly unexplored strong-coupling regime of pronounced phase fluctuations. In the latter, two characteristic temperatures T(*) and T(c), associated with short- and long-range ordering, respectively, can be identified in a mean-field-motivated Hamiltonian. T(*) at the same time corresponds to the opening of a gap in the excitation spectrum. In addition to introducing a novel procedure to study strongly coupled d-wave superconductors, our results indicate that classical phase fluctuations are not sufficient to explain the pseudogap features of high-temperature superconductors.     

Fluctuation-driven first-order transition in Pauli-limited d-wave superconductors

We study the phase transition between the normal and nonuniform (Fulde-Ferrell-Larkin-Ovchinnikov) superconducting state in quasi-two-dimensional d-wave superconductors at finite temperature. We obtain an appropriate Ginzburg-Landau theory for this transition, in which the fluctuation spectrum of the order parameter has a set of minima at nonzero momenta. The momentum shell renormalization group procedure combined with epsilon expansion is then applied to analyze the phase structure of the theory. We find that all fixed points have more than one relevant direction, indicating the transition is of the fluctuation-driven first-order type for this universality class.