Edge Current due to Majorana Fermions in Superfluid 3^3He A- and B-Phases

We propose a method utilizing edge current to observe Majorana fermions in the surface Andreev bound state for the superfluid $^3$He A- and B-phases. The proposal is based on self-consistent analytic solutions of quasi-classical Green's function with an edge. The local density of states and edge mass current in the A-phase or edge spin current in the B-phase can be obtained from these solutions. The edge current carried by the Majorana fermions is partially cancelled by quasiparticles (QPs) in the continuum state outside the superfluid gap. QPs contributing to the edge current in the continuum state are distributed in energy even away from the superfluid gap. The effect of Majorana fermions emerges in the depletion of the edge current by temperature within a low-temperature range. The observations that the reduction in the mass current is changed by $T^2$-power in the A-phase and the reduction in the spin current is changed by $T^3$-power in the B-phase establish the existence of Majorana fermions. We also point out another possibility for observing Majorana fermions by controlling surface roughness.Comment: 13 pages, 4 figures, published versio

Rough Surface Effect on Meissner Diamagnetism in Normal-layer of N-S Proximity-Contact System

Rough surface effect on the Meissner diamagnetic current in the normal layer of proximity contact N-S bi-layer is investigated in the clean limit. The diamagnetic current and the screening length are calculated by use of quasi-classical Green's function. We show that the surface roughness has a sizable effect, even when a normal layer width is large compared with the coherence length $\xi =v_{\rm F}/\pi T_{\rm c}$. The effect is as large as that of the impurity scattering and also as that of the finite reflection at the N-S interface.Comment: 12 pages, 3 figures. To be published in J. Phys. Soc. Jpn. Vol.71-

Strong Anisotropy in Spin Suceptibility of Superfluid 3He-B Film Caused by Surface Bound States

Spin susceptibility of superfluid 3He-B film with specular surfaces is calculated. It is shown that, when the magnetic field is applied in a direction perpendiculr to the film, the suseptibility is significantly enhanced by the contribution from the surface bound states. No such enhancement is found for the magnetic field parallel to the film. A simplified model with spatially constant order parameter is used to elucidate the magnetic properties of the surface bound states. The Majorana nature of the zero energy bound state is also mentioned.Comment: 4 pages, 4 figure

Quasiclassical theory of superconductivity: a multiple interface geometry

The purpose of the paper is to suggest a new method which allows one to study multiple coherent reflection/transmissions by partially transparent interfaces (e.g. in multi-layer mesoscopic structures or grain boundaries in high-Tc's) in the framework of the quasiclassical theory of superconductivity. It is argued that typically the trajectory of the particle is a simply connected tree (no loops) with knots, i.e. the points where interface scattering events occur and ballistic pieces of the trajectory are mixed. A linear boundary condition for the 2-component trajectory "wave function" which factorizes matrix (retarded) Green's function, is formulated for an arbitrary interface, specular or diffusive. To show the usage of the method, the current response to the vector potential (the total superfluid density rho_s) of a SS' sandwich with the different signs of the order parameter in S and S', is calculated. In this model, a few percent of reflection by the SS' interface transforms the paramagnetic response (rho_s < 0) created by the zero-energy Andreev bound states near an ideal interface (see Fauchere et al. PRL, 82, 3336 (1999), cond-mat/9901112), into the usual diamagnetic one (rho_s >0).Comment: Extended abstract submitted to "Electron Transport in Mesoscopic Systems", Satellite conference to LT22, Goteborg, 12-15 August, 1999. 2 pages Minor changes + the text height problem fixe

Domain Walls in Superfluid 3He-B

We consider domain walls between regions of superfluid 3He-B in which one component of the order parameter has the opposite sign in the two regions far from one another. We report calculations of the order parameter profile and the free energy for two types of domain wall, and discuss how these structures are relevant to superfluid 3He confined between two surfaces.Comment: 6 pages with 3 figures. Conference proceedings of QSF 2004, Trento, Ital

Thermodynamic properties of thin films of superfluid 3He-A

The pairing correlations in superfluid He-3 are strongly modified by quasiparticle scattering off a surface or an interface. We present theoretical results and predictions for the order parameter, the quasiparticle excitation spectrum and the free energy for thin films of superfluid He-3. Both specular and diffuse scattering by a substrate are considered, while the free surface is assumed to be a perfectly reflecting specular boundary. The results are based on self-consistent calculations of the order parameter and quasiparticle excitation spectrum at zero pressure. We obtain new results for the phase diagram, free energy, entropy and specific heat of thin films of superfluid He-3.Comment: Replaced with an updated versio

Density of states in d-wave superconductors of finite size

We consider the effect of the finite size in the ab-plane on the surface density of states (DoS) in clean d-wave superconductors. In the bulk, the DoS is gapless along the nodal directions, while the presence of a surface leads to formation of another type of the low-energy states, the midgap states with zero energy. We demonstrate that finiteness of the superconductor in one of dimensions provides the energy gap for all directions of quasiparticle motion except for \theta=45 degrees (\theta is the angle between the trajectory and the surface normal); then the angle-averaged DoS behaves linearly at small energies. This result is valid unless the crystal is 0- or 45-oriented (\alpha \ne 0 or 45 degrees, where \alpha is the angle between the a-axis and the surface normal). In the special case of \alpha=0, the spectrum is gapped for all trajectories \theta; the angle-averaged DoS is also gapped. In the special case of \alpha=45, the spectrum is gapless for all trajectories \theta; the angle-averaged DoS is then large at low energies. In all the cases, the angle-resolved DoS consists of energy bands that are formed similarly to the Kronig-Penney model. The analytical results are confirmed by a self-consistent numerical calculation.Comment: 9 pages (including 5 EPS figures), REVTeX