No abstract

Several recent experiments find evidence of superfluidity of 3 He in 98%-porous aerogel. The primary effect of the aerogel is that it scatters the quasiparticles of 3 He. We find that many experimental findings are quantitatively understood by a relatively simple model that takes into account strong inhomogeneity of the scattering on a length scale of 100 nm. PACS: 74.25.Fy, 74.70.Tx, 72.15.Eb The discovery of unconventional paring states in hightemperature superconductors has generated a lot of interest in impurity scattering in these materials. In particular, the inhomogeneity of the scattering has been considered recently [1]. However, both the experimental and theoretical studies are difficult because of the complicated structure of these substances. Recently, a new possibility was opened for studying impurity effects on unconventional pairing states: superfluid 3 He in very porous aerogel. This system has many advantages. For example, the pure state of superfluid 3 He is absolutely pure in experiments, and it is theoretically very well understood. A crucial parameter, the coherence length ξ 0 , can easily be varied within a factor 5 by varying the pressure. The torsional oscillator experiments [2,3] and NMR experiments [4] measure directly such basic quantities as the superfluid density, the pairing amplitude and the spin susceptibility.In this letter we give theoretical explanations for some of the experimental observations on superfluid 3 He in aerogel. As a first attempt we study a model, where the aerogel is assumed as a homogeneous scatterer of the quasiparticles of 3 He. This model gives predictions with a correct tendency, but it is insufficient quantitatively. A "slab model" gives a clue that the inhomogeneity of the scattering is crucial for understanding the discrepancy. Based on that we construct a relatively simple model of inhomogeneous scattering that quantitatively can explain both the transition temperature and the pairing amplitude, and predicts an inhomogeneity length scale of 100 nm. We also consider the upper limit for anisotropic scattering set by the NMR measurements.In the experiments the aerogel fills only 2% of the total volume (V = 0.02), and its surface to volume ratio is A = 260, 000 cm −1 [5]. Assuming naively that the material consists of a network of one-dimensional strands, we can from these numbers alone estimate the strand diameter 4V /A = 3 nm. The distance between strands is √ 4πV /A = 20 nm. The mean free path for straight line trajectories is estimated as ℓ = 4/A = 150 nm. This is also the mean free path for quasiparticles of 3 He when the aerogel is filled with 3 He at millikelvin temperatures. Quasiclassical theory.-Because the volume fraction of the aerogel strands (including an inert layer of 3 He atoms on the strands) is small, we neglect all effects that are linear in the volume fraction. In particular, we assume that the density, the Landau Fermi-liquid parameters, the coupling constant of the pairing interaction, and the dipole-dipole interaction constant are...

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

The superconducting gap function of Sr2RuO4 was investigated by means of quasiparticle reflection and transmission at the normal conductor-superconductor interface of Sr2RuO4-Pt point contacts. We found two distinctly different types of dV /dI vs V spectra either with a double-minimum structure or with a zero-bias conductance anomaly. Both types of spectra are expected in the limit of high and low transparency, respectively, of the interface barrier between a normal metal and a spin-triplet superconductor. Together with the temperature dependence of the spectra this result strongly supports a spin-triplet superconducting order parameter for Sr2RuO4. 74.70.Dd, 71.20.Lp, 73.40.Jn, 74.80.Fp

Theoretical results for the ab-plane tunneling conductance in the d-wave model for high-T c superconductors are presented. The d-wave model predicts surface bound states below the maximum gap. A subdominant order parameter, stabilized by the surface, leads to a splitting of the zero-bias conductance peak (ZBCP) in zero external field and to spontaneous surface currents. In a magnetic field, screening currents shift the bound state spectrum, leading to a splitting of the ZBCP that is linear in H at low fields and saturates at a pair breaking critical field of order H ‫ء‬ c Ӎ 3 T. [S0031-9007 (97)03527-8] PACS numbers: 74.50. + r, 74.72.Bk In the d x 2 2y 2 model for the cuprate superconductors surface states are predicted which should be observable in the subgap conductance for ab-plane tunneling [1-3]. Observations of a zero-bias peak (ZBCP) in the in-plane coductance were reported for tunnel junctions on oriented YBa 2 Cu 3 O 72d (YBCO) films by Geerk et al. [4], Lesueur et al. [5], and Covington et al. [6]. The ZBCP splits in a magnetic field of a few tesla, and recent experiments show that a splitting of a few meV also appears at low temperatures in zero field [7]. The identification of the ZBCP with surface bound states associated with d-wave pairing is important because the origin of the ZBCP in the ab-plane tunneling conductance is the same as that of the p phase shift in the Josephson interference experiments [8]. The same sign change that leads to a p phase shift in the Josephson current-phase relation is also responsible for a ZBCP in the ab-plane quasiparticle tunneling conductance for high impedance junctions [1][2][3]. The ZBCP is observed with comparable magnitude for both (110) and (100) orientated surfaces [6], whereas theoretical calculations [1-3] predicted no ZBCP for (100) interfaces. We show that a large ZBCP is expected in the ab-plane tunneling conductance for all orientations if the interface is microscopically rough.Several authors have suggested that the surface of dwave superconductors might exhibit spontaneously generated surface currents associated with the presence of a second superconducting order parameter [9,10]. The surface state of any d x 2 2y 2 superconductor will exhibit a spontaneously broken time-reversal symmetry phase at sufficiently low temperature (Ref.[3] and below). The tunneling spectrum for current-carrying states of d-wave superconductors, externally imposed and spontaneously generated, is the main subject of this Letter.When an excitation reflects elastically off a (110) surface its momentum changes, p f ! p f . Incident and reflected wave packets propagate through different order parameter fields, D͑p f , R͒ vs D͑p f , R͒, which leads to Andreev scattering, a process of "retroreflection" in which a particlelike excitation undergoes branch conversion into a holelike excitation with reversed group velocity. Bound states occur at energies for which the phases of Andreevreflected particlelike and holelike excitations interfere constructively. This effect is pronounced...

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

We investigate electromagnetic radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. At frequencies below the well-known emission peak at the Josephson frequency (2eV/h), extra radiation is triggered by quantum fluctuations in the transmission line. For weak tunneling couplings and typical Ohmic transmission lines, the corresponding photon-flux spectrum is symmetric around half the Josephson frequency, indicating that the photons are predominately created in pairs. By establishing an input-output formalism for the microwave field in the transmission line, we give further evidence for this nonclassical photon pair production, demonstrating that it violates the classical Cauchy-Schwarz inequality for two-mode flux cross correlations. In connection to recent experiments, we also consider a stepped transmission line, where resonances increase the signal-to-noise ratio.

We present an extensive experimental and theoretical study of the proximity effect in InAs nanowires connected to superconducting electrodes. We fabricate and investigate devices with suspended gate-controlled nanowires and nonsuspended nanowires, with a broad range of lengths and normal-state resistances. We analyze the main features of the current-voltage characteristics: the Josephson current, excess current, and subgap current as functions of length, temperature, magnetic field, and gate voltage, and compare them with theory. The Josephson critical current for a short-length device, L = 30 nm, exhibits a record high magnitude of 800 nA at low temperature that comes close to the theoretically expected value. The critical current in all other devices is typically reduced compared to the theoretical values. The excess current is consistent with the normal resistance data and agrees well with the theory. The subgap current shows a large number of structures; some of them are identified as subharmonic gap structures generated by multiple Andreev reflection. The other structures, detected in both suspended and nonsuspended devices, have the form of voltage steps at voltages that are independent of either the superconducting gap or length of the wire. By varying the gate voltage in suspended devices, we are able to observe a crossover from typical tunneling transport at large negative gate voltage, with suppressed subgap current and negative excess current, to pronounced proximity junction behavior at large positive gate voltage, with enhanced Josephson current and subgap conductance as well as a large positive excess current.