Broadening of Andreev-Bound States in d_{x^2-y^2} superconductors

We investigate the broadening of the bound states at an interface of an unconventional superconductor by bulk impurity scattering. We use the quasiclassical theory and include impurity scattering in the Born and in the unitarity limit. The broadening of bound states due to unitary scatterers is shown to be substantially weaker than in the Born limit. We study various model geometries and calculate the temperature dependence of the Josephson critical current in the presence of these impurity-broadened bound states.Comment: 6 page including 7 figures, submitted to Phys. Rev.

Subharmonic gap structure in d-wave superconductors

We present a self-consistent theory of current-voltage characteristics of d-wave/d-wave contacts at arbitrary transparency. In particular, we address the open problem of the observation of subharmonic gap structure (SGS) in cuprate junctions. Our analysis shows that: (i) the SGS is possible in d-wave superconductors, (ii) the existence of bound states within the gap results in an even-odd effect in the SGS, (iii) elastic scattering mechanisms, like impurities or surface roughness, may suppress the SGS, and (iv) in the presence of a magnetic field the Doppler shift of the Andreev bound states leads to a very peculiar splitting of the SGS, which is an unambiguous fingerprint of d-wave superconductivity.Comment: Revtex4, 4 pages, 5 figure

Two regimes for effects of surface disorder on the zero-bias conductance peak of tunnel junctions involving d-wave superconductors

Impurity-induced quasiparticle bound states on a pair-breaking surface of a d-wave superconductor are theoretically described, taking into account hybridization of impurity- and surface-induced Andreev states. Further a theory for effects of surface disorder (of thin impurity surface layer) on the low-bias conductance of tunnel junctions is developed. We find a threshold $n_c$ for surface impurity concentration $n_S$, which separates the two regimes for surface impurity effects on the zero-bias conductance peak (ZBCP). Below the threshold, surface impurities do not broaden the ZBCP, but effectively reduce its weight and generate impurity bands. For low $n_S$ impurity bands can be, in principle, resolved experimentally, being centered at energies of bound states induced by an isolated impurity on the surface. For larger $n_S$ impurity bands are distorted, move to lower energies and, beginning with the threshold concentration $n_S=n_c$, become centered at zero energy. With increasing $n_S$ above the threshold, the ZBCP is quickly destroyed in the case of strong scatterers, while it is gradually suppressed and broaden in the presence of weak impurity potentials. More realistic cases, taking into account additional broadening, not related to the surface disorder, are also considered.Comment: 9 pages, 7 figure

Shot noise in normal metal-d-wave superconducting junctions

We present theoretical calculations and predictions for the shot noise in voltage biased junctions of $d_{x^2-y^2}$ superconductors and normal metal counter-electrodes. In the clean limit for the d-wave superconductor the shot noise vanishes at zero voltage because of resonant Andreev reflection by zero-energy surface bound states. We examine the sensitivity of this resonance to impurity scattering. We report theoretical results for the magnetic field dependence of the shot noise, as well the fingerprints of subdominant $s$- and $d_{xy}$ pairing channels.Comment: 15 pages, 8 figures and 3 tables embedde

Andreev reflection in layered structures: implications for high T_c grain boundary Josephson junctions

Andreev reflection is investigated in layered anisotropic normal metal / superconductor (N/S) systems in the case of an energy gap \Delta in S not negligible with respect to the Fermi energy E_F, as it probably occurs with high critical temperature superconductors (HTS). We find that in these limits retro-reflectivity, which is a fundamental feature of Andreev reflection, is broken modifying sensitively transport across S/N interfaces. We discuss the consequences for supercurrents in HTS Josephson junctions and for the midgap states in S-N contactsComment: 4 pages, 4 figures, to be published in Phys. Rev.

D-Wave Superconductors near Surfaces and Interfaces: A Scattering Matrix Approach within the Quasiclassical Technique

A recently developed method [A. Shelankov and M. Ozana, Phys. Rev. B 61, 7077 (2000)] is applied to investigate d-wave superconductors in the vicinity of (rough) surfaces. While this method allows the incorporation of arbitrary interfaces into the quasiclassical technique, we discuss, as examples, diffusive surfaces and boundaries with small tilted mirrors (facets). The properties of the surface enter via the scattering matrix in the boundary condition for the quasiclassical Green's function. The diffusive surface is described by an ensemble of random scattering matrices. We find that the fluctuations of the density of states around the average are small; the zero bias conductance peak broadens with increasing disorder. The faceted surface is described in the model where the scattering matrix couples m in- and m out-trajectories (m>=2). No zero bias conductance peak is found for [100] surfaces; the relation to the model of Fogelstrom et al. [Phys. Rev. Lett. 79, 281 (1997)] is discussed.Comment: RevTeX, 19 pages, 18 figure

Quasiparticle Interface States in Junctions Involving d-Wave Superconductors

Influence of surface pair breaking, barrier transmission and phase difference on quasiparticle bound states in junctions with d-wave superconductors is examined. Based on the quasiclassical theory of superconductivity, an approach is developed to handle interface bound states. It is shown in SIS' junctions that low energy bound states get their energies reduced by surface pair breaking, which can be taken into account by introducing an effective order parameter for each superconductor at the junction barrier. More interestingly, for the interface bound states near the continuous spectrum the effect of surface pair breaking may result in a splitting of the bound states. In the tunneling limit this can lead to a square root dependence of a nonequilibrium Josephson current on the barrier transmision, which means an enhancement as compared to the conventional critical current linear in the transmission. Reduced broadening of bound states in NIS junctions due to surface pair breaking is found.Comment: 27 pages, Latex fil

Disordered Josephson Junctions of d-Wave Superconductors

We study the Josephson effect between weakly coupled d-wave superconductors within the quasiclassical theory, in particular, the influence of interface roughness on the current-phase relation and the critical current of mirror junctions and $45^\circ$ asymmetric junctions. For mirror junctions the temperature dependence of the critical current is non-monotonic in the limit of low roughness, but monotonic for very rough interfaces. For $45^\circ$ asymmetric junctions with a linear dimension much larger than the superconducting coherence length we find a $\sin(2\phi)$-like current-phase relation, whereas for contacts on the scale of the coherence length or smaller the usual $\sin\phi$-like behavior is observed. Our results compare well with recent experimental observations.Comment: 10 pages, 12 figures; accepted for publication in Phys. Rev.

Josephson currents through spin-active interfaces

The Josephson coupling of two isotropic s-wave superconductors through a small, magnetically active junction is studied. This is done as a function of junction transparency and of the degree of spin-mixing occurring in the barrier. In the tunneling limit, the critical current shows an anomalous 1/T temperature dependence at low temperatures and for certain magnetic realizations of the junction. The behavior of the Josephson current is governed by Andreev bound states appearing within the superconducting gap and the position of these states in energy is tunable with the magnetic properties of the barrier. This study is done using the equilibrium part of the quasiclassical Zaitsev-Millis-Rainer-Sauls boundary condition for spin-active interfaces and a general solution of the boundary condition is found. This solution is a generalization of the one recently presented by Eschrig [M. Eschrig, Phys. Rev B 61, 9061 (2000)] for spin-conserving interfaces and allows an effective treatment of the problem of a superconductor in proximity to a magnetically active material.Comment: 8 pages + 3 eps figure

Quasiclassical description of transport through superconducting contacts

We present a theoretical study of transport properties through superconducting contacts based on a new formulation of boundary conditions that mimics interfaces for the quasiclassical theory of superconductivity. These boundary conditions are based on a description of an interface in terms of a simple Hamiltonian. We show how this Hamiltonian description is incorporated into quasiclassical theory via a T-matrix equation by integrating out irrelevant energy scales right at the onset. The resulting boundary conditions reproduce results obtained by conventional quasiclassical boundary conditions, or by boundary conditions based on the scattering approach. This formalism is well suited for the analysis of magnetically active interfaces as well as for calculating time-dependent properties such as the current-voltage characteristics or as current fluctuations in junctions with arbitrary transmission and bias voltage. This approach is illustrated with the calculation of Josephson currents through a variety of superconducting junctions ranging from conventional to d-wave superconductors, and to the analysis of supercurrent through a ferromagnetic nanoparticle. The calculation of the current-voltage characteristics and of noise is applied to the case of a contact between two d-wave superconductors. In particular, we discuss the use of shot noise for the measurement of charge transferred in a multiple Andreev reflection in d-wave superconductors