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-

Spin susceptibility of the superfluid 3^{3}He-B in aerogel

The temperature dependence of paramagnetic susceptibility of the superfluid ^{3}He-B in aerogel is found. Calculations have been performed for an arbitrary phase shift of s-wave scattering in the framework of BCS weak coupling theory and the simplest model of aerogel as an aggregate of homogeneously distributed ordinary impurities. Both limiting cases of the Born and unitary scattering can be easily obtained from the general result. The existence of gapless superfluidity starting at the critical impurity concentration depending on the value of the scattering phase has been demonstrated. While larger than in the bulk liquid the calculated susceptibility of the B-phase in aerogel proves to be conspicuously smaller than that determined experimentally in the high pressure region.Comment: 10 pages, 4 figures, REVTe

Spontaneous magnetization and Hall effect in superconductors with broken time-reversal symmetry

Broken time reversal symmetry (BTRS) in d wave superconductors is studied and is shown to yield current carrying surface states. The corresponding spontaneous magnetization is temperature independent near the critical temperature Tc for weak BTRS, in accord with recent data. For strong BTRS and thin films we expect a temperature dependent spontaneous magnetization with a paramagnetic anomaly near Tc. The Hall conductance is found to vanish at zero wavevector q and finite frequency w, however at finite q,w it has an unusual structure.Comment: 7 pages, 1 eps figure, Europhysics Letters (in press

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

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

Overscreening Diamagnetism in Cylindrical Superconductor-Normal Metal-Heterostructures

We study the linear diamagnetic response of a superconducting cylinder coated by a normal-metal layer due to the proximity effect using the clean limit quasiclassical Eilenberger equations. We compare the results for the susceptibility with those for a planar geometry. Interestingly, for $R\sim d$ the cylinder exhibits a stronger overscreening of the magnetic field, i.e., at the interface to the superconductor it can be less than (-1/2) of the applied field. Even for $R\gg d$, the diamagnetism can be increased as compared to the planar case, viz. the magnetic susceptibility $4\pi\chi$ becomes smaller than -3/4. This behaviour can be explained by an intriguing spatial oscillation of the magnetic field in the normal layer

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