Yasushi Nagato

Theory of the Andreev reflection and the density of states in proximity contact normal-superconducting infinite double-layer

Proximity contact N-S double-layer with infinite layer widths is studied in the clean limit. The finite reflection at the interface is taken into account. Starting from a recent theory of finite width double-layer by Ashida et al., we obtain explicit expressions for the quasi-classical Greens function which already satisfy the boundary condition and include no exploding terms at infinities. The self-consistent pair potentials are obtained numerically with sufficient accuracy. The Andreev reflection at the N-S interface is discussed on the basis of the self-consistent pair potential. It is shown that there exists a resonance state in a potential valley formed between the depressed pair potential and the partially reflecting interface, which leads to a peak of the Andreev reflection coefficient with the height unity slightly below the bulk superconductor energy gap. We also find general relationship between the Andreev reflection coefficient and the local density of states of the superconductor just at the interface.

Rough Surface Effects on the p-Wave Fermi Superfluids

Rough surface effects on p-wave Fermi superfluids are discussed on the basis of our recently proposed quasi-classical theory that can treat in a unified way the surface scattering ranging from the specular limit to the diffusive limit. We show how the transition temperature of the ABM state in a slab geometry depends on the surface roughness. In the diffusive limit, our result agrees with Kjäldmann et al. We consider the BW state, the ABM state and the polar state in a half-infinite geometry with a plane rough surface and discuss the self-consistent order parameter and the surface density of states at low temperatures. The rough surface effects on the Andreev scattering in the BW state are also discussed within the same framework.

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

Spin susceptibility of superfluid 3 He-B film with specular surfaces is calculated on the basis of the self consistent order parameter. It is shown that, when the magnetic field is applied in a direction perpendicular 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.

Theory of rough surface effects on the anisotropic BCS states

We present a Greens function theory of the rough surface effects on the anisotropic BCS states using the formulation developed in the randomly rippled wall model. It is shown that the randomly rippled wall formulation is general enough to treat rough surface effects from the specular limit to the diffusive limit. We propose a statistical wall configuration such that gives the diffusive limit in the normal state. Within the weak coupling theory, we give a formal solution of the quasi-classical Greens function in a slab geometry and in a semi-infinite geometry with arbitrarily rough surfaces. The formal solution already satisfies the boundary condition. In the diffusive limit, the present theory correctly recovers the linearized gap equation obtained by Kjäldman et al. for the p-wave state in a slab geometry.

Surface Majorana cone of the superfluid 3He B phase

The superfluid 3 He B phase, one of the oldest unconventional fermionic condensates experimentally realized, is recently predicted to support Majorana fermion surface states. Majorana fermion, which is characterized by the equivalence of particle and antiparticle, has a linear dispersion relation referred to as the Majorana cone. We measured the transverse acoustic impedance Z of the superfluid 3 He B phase changing its boundary condition and found a growth of peak in Z on a higher specularity wall. Our theoretical analysis indicates that the variation of Z is induced by the formation of the cone-like dispersion relation and thus confirms the important feature of the Majorana fermion in the specular limit.

Rough surface effects on d-wave superconductors

We present a quasi-classical Greens function theory for the rough surface effects on d -wave BCS states. We reformulate and generalize the randomly rippled wall model of rough surfaces so that it can describe the surface scattering ranging from the specular limit to the diffusive limit. We give a formal solution of the quasi-classical Greens function in a semi-infinite geometry with arbitrarily rough surfaces. The formal solution satisfies the boundary condition. We apply this method to the two-dimensional d x 2 - y 2 and d x y states and show how the self-consistent order parameter and the surface density of states change according to the surface roughness. The present analysis is relevant to tunneling spectroscopy of cuprate superconductors through the surfaces parallel to the c -axis.

Phase Diagram of the Fulde-Ferrell-Larkin-Ovchinnikov State in a Three-Dimensional Superconductor

The phase diagram of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a 3-dimensional superconductor is discussed. We use the quasi-classical Greens function to calculate the free energy. It is shown that the phase transition from the normal state is of first order at high temperatures but is of second order near T =0. To describe the phase transition in the Ginzburg-Landau theory, one has to take into account up to eighth order term with respect to the order parameter. The phase transition from the FFLO state to the uniform superconducting state is of second order in all the temperature range T <0.561 T c in accordance with Burkhardt and Rainers result in a 2-dimensional system.

Subgap in the Edge States of Two-Dimensional Chiral Superconductor with Rough Surface

We discuss the rough surface effects on a two-dimensional chiral k x +i k y superconductor. The atomic scale roughness at the surface is considered using the random S matrix model. The roughness effects on the self-consistent order parameter, surface mass current, and surface density of states are studied using the quasi-classical theory. We find that the surface mass current is suppressed by the surface roughness. The surface density of states shows quite a similar behavior to that of the superfluid 3 He B phase. When the surface is specular, the surface Andreev bound states form a band that fills the bulk energy gap Δ bulk . When the surface becomes diffusive, there occurs a sharp upper edge of the surface bound states band and there opens a subgap between the edge and the bulk energy gap. We show that this subgap is induced by the repulsion between the surface bound states and the propagating Bogoliubov quasi-particles through the second order process of roughness.

Odd-frequency Cooper pairs and zero-energy surface bound states in superfluid 3He

He. The odd-frequency pair amplitude is closely related to the local density of states in the low energy limit. Wederive a formula relating explicitly the two quantities. This formula holds for arbitrary boundarycondition at the surface. We also present some numerical results on the surface odd-frequency pairamplitude in superfluid

A–B transition of superfluid 3He in a slab with rough surfaces

Abstract We discuss the A–B transition of superfluid 3 He in a slab with rough surfaces using the quasi-classical theory in the weak coupling approximation. The superfluid transition temperature is presented as a function of the slab width for various roughness parameters. The surface roughness suppresses the A phase order parameter parallel to the surfaces, and thus favors the B phase. This agrees with the results of a Ginzburg–Landau theory by Li and Ho.