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

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

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

Quasiparticle Bound States and Low-Temperature Peaks of the Conductance of NIS Junctions in d-Wave Superconductors

Quasiparticle states bound to the boundary of anisotropically paired superconductors, their contributions to the density of states and to the conductance of NIS junctions are studied both analytically and numerically. For smooth surfaces and real order parameter we find some general results for the bound state energies. In particular, we show that under fairly general conditions quasiparticle states with nonzero energies exist for momentum directions within a narrow region around the surface normal. The energy dispersion of the bound states always has an extremum for the direction along the normal. Along with the zero-bias anomaly due to midgap states, we find, for quasi two-dimensional materials, additional low-temperature peaks in the conductance of NIS junctions for voltages determined by the extrema of the bound state energies. The influence of interface roughness on the conductance is investigated within the framework of Ovchinnikov's model. We show that nonzero-bias peaks at low temperatures may give information on the order parameter in the bulk, even though it is suppressed at the surface.Comment: 14 pages, PostScrip

Topology of Andreev Bound States with Flat Dispersion

A theory of dispersionless Andreev bound states on surfaces of time-reversal invariant unconventional superconductors is presented. The generalized criterion for the dispersionless Andreev bound state is derived from the bulk-edge correspondence, and the chiral spin structure of the dispersionless Andreev bound states is argued from which the Andreev bound state is stabilized. Then we summarize the criterion in a form of index theorems. The index theorems are proved in a general framework to certify the bulk-edge correspondence. As concrete examples, we discuss (i) dxy-wave superconductor (ii) px-wave superconductor, and (iii) noncentrosymmetric superconductors. In the last example, we find a peculiar time-reversal invariant Majorana fermion. The time-reversal invariant Majorana fermion shows an unusual response to the Zeeman magnetic field, which can be used to identify it experimentally.Comment: 56 pages, 11 figures, references are adde

Phase-Sensitive Impurity Effects in Vortex Core of Moderately Clean Chiral Superconductors

We study impurity effects in vortex core of two-dimensional moderately clean su perconductors within the quasiclassical theory. The impurity scattering rate \G amma(E) of the Andreev bound states in vortex core with +1 vorticity of p-wav e superconductors with {\mib d}=\hat{\mib z}(p_x+\iu p_y) is suppre ssed, compared to the normal state scattering rate $\Gamma_{\rm n}$ in the energ y region \Gamma_{\rm n}^3/E_\delta^2\ll E\ll E_\delta\equiv |\delta_0|\Delta_\i nfty with scattering phase shift $\delta_0$ $(|\delta_0|\ll 1)$ and the pair-po tential in bulk $\Delta_\infty$. Further we find that $\Gamma(E)/\Gamma_{\rm n}$ for p-wave superconductors with {\mib d}=\hat{\mib z}(p_x-\iu p_y) is at most {\cal O}(E/\Delta_\i nfty). These results are in marked contrast to the even-parity case (s,d-wave), where $\Gamma(E)/\Gamma_{\rm n}$ is known to be proportional to \ln(\Delta_\i nfty/E) . Parity- and chirality-dependences of impurity effects are attributed to the Andr eev reflections involved in the impurity-induced scattering between bound states . Implications for the flux flow conductivity is also discussed. Novel enhanceme nt of flux flow conductivity is expected to occur at $T\ll E_\delta$ for {\mib d}=\hat{\mib z}(p_x+\iu p_y) and at $T\ll \Delta_\infty$ for {\mib d}=\hat{\mib z}(p_x-\iu p_y).Comment: 9 pages, No figures, To appear in JPSJ Vol. 69, No. 10 (2000

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

Anastomoses entre nervo mediano e nervo ulnar no antebraço

O estudo das anastomoses entre nervo mediano e nervo ulnar no antebraço denota grande atenção pela sua incidência e sua grande importância clínica, principalmente no correto diagnóstico de neuropatias periféricas. A importância de sua verificação e delimitação se dá como forma de evitar lesões em procedimentos cirúrgicos e na reabilitação de pacientes portadores de patologias do membro superior. Entre as anastomoses pode-se encontrar anastomose do tipo mediano-ulnar, também conhecida como anastomose de Martin-Gruber de incidência relativamente alta; e a anastomose do tipo ulnar-mediano, ou anastomose de Marinacci; esta de incidência bem mais baixa. O presente estudo tem como intuito relatar a incidência, os tipos de anastomoses encontradas, sua topografia e aferir o comprimento dessas anastomoses. Foram dissecados 30 antebraços do Instituto de Anatomia da Universidade Severino Sombra para verificação de incidência e do comprimento dessas anastomoses, sendo esse aferido com auxílio de uma Trena (3M). Foram encontradas 3(três) cadáveres que continham a anastomose de Martin-Gruber com média de comprimento de 6,6 cm e 1(um) cadáver que continha a anastomose de Marinacci com comprimento de 7,4 cm, esta de baixa incidência na literatura, sendo corroborado com o presente estudo.Com isso pode-se observar no presente estudo uma prevalência da Anastomose de Martin-Gruber em relação a anastomose de Marinacci, sendo seu comprimento médio de 6,6 cm

Nonmagnetic impurity effects in MgB2_{2}

We study nonmagnetic impurity effects in MgB$_{2}$ using the quasiclassical equations of superconductivity for a weak-coupling two-band model. Parameters in the model are fixed so as to reproduce experiments on MgB$_{2}$ as closely as possible. The quasiparticle density of states and the specific heat are calculated for various values of the interband impurity scattering. The density of states changes gradually from a two-gap structure into the conventional single-gap structure as the interband scattering increases. It is found that the excitation threshold is not a monotonic function of the interband scattering. Calculated results for the specific heat are in good agreements with experiments on samples after irradiation