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

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-

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

Electronic structure of d-wave superconducting quantum wires

We present analytical and numerical results for the electronic spectra of wires of a d-wave superconductor on a square lattice. The spectra of Andreev and other quasiparticle states, as well as the spatial and particle-hole structures of their wave functions, depend on interference effects caused by the presence of the surfaces and are qualitatively different for half-filled wires with even or odd number of chains. For half-filled wires with an odd number of chains N at (110) orientation, spectra consist of N doubly degenerate branches. By contrast, for even N wires, these levels are split, and all quasiparticle states, even the ones lying above the maximal gap, have the characteristic properties of Andreev bound states. These Andreev states above the gap can be interpreted as a consequence of an infinite sequence of Andreev reflections experienced by quasiparticles along their trajectories bounded by the surfaces of the wire. Our microscopic results for the local density of states display atomic-scale Friedel oscillations due to the presence of the surfaces, which should be observable by scanning tunneling microscopy. For narrow wires the self-consistent treatment of the order parameter is found to play a crucial role. In particular, we find that for small wire widths the finite geometry may drive strong fluctuations or even stablilize exotic quasi-1D pair states with spin triplet character.Comment: 21 pages, 20 figures. Slightly modified version as published in PR

Majorana edge modes of superfluid 3He A-phase in a slab

Motivated by a recent experiment on the superfluid 3He A-phase with a chiral p-wave pairing confined in a thin slab, we propose designing a concrete experimental setup for observing the Majorana edge modes that appear around the circumference edge region. We solve the quasi-classical Eilenberger equation, which is quantitatively reliable, to evaluate several observables. To derive the property inherent to the Majorana edge state, the full quantum mechanical Bogoliubov-de Gennes equation is solved in this setting. On the basis of the results obtained, we perform decisive experiments to check the Majorana nature.Comment: 5 pages, 5 figure