A Discrete Version of the Inverse Scattering Problem and the J-matrix Method

The problem of the Hamiltonian matrix in the oscillator and Laguerre basis construction from the S-matrix is treated in the context of the algebraic analogue of the Marchenko method.Comment: 11 pages. The Laguerre basis case is adde

Quasiclassical approach to the spin-Hall effect in the two-dimensional electron gas

We study the spin-charge coupled transport in a two-dimensional electron system using the method of quasiclassical ($\xi$-integrated) Green's functions. In particular we derive the Eilenberger equation in the presence of a generic spin-orbit field. The method allows us to study spin and charge transport from ballistic to diffusive regimes and continuity equations for spin and charge are automatically incorporated. In the clean limit we establish the connection between the spin-Hall conductivity and the Berry phase in momentum space. For finite systems we solve the Eilenberger equation numerically for the special case of the Rashba spin-orbit coupling and a two-terminal geometry. In particular, we calculate explicitly the spin-Hall induced spin polarization in the corners, predicted by Mishchenko et al. [13]. Furthermore we find universal spin currents in the short-time dynamics after switching on the voltage across the sample, and calculate the corresponding spin-Hall polarization at the edges. Where available, we find perfect agreement with analytical results.Comment: 9 pages, 6 figure

Chirality sensitive effect on surface states in chiral p-wave superconductors

We study the local density of states at the surface of a chiral p-wave superconductor in the presence of a weak magnetic field. As a result, the formation of low-energy Andreev bound states is either suppressed or enhanced by an applied magnetic field, depending on its orientation with respect to the chirality of the p-wave superconductor. Similarly, an Abrikosov vortex, which is situated not too far from the surface, leads to a zero-energy peak of the density of states, if its chirality is the same as that of the superconductor, and to a gap structure for the opposite case. We explain the underlying principle of this effect and propose a chirality sensitive test on unconventional superconductors.Comment: 4 pages, 2 figure

Quasiparticle states of the Hubbard model near the Fermi level

The spectra of the t-U and t-t'-U Hubbard models are investigated in the one-loop approximation for different values of the electron filling. It is shown that the four-band structure which is inherent in the case of half-filling and low temperatures persists also for some excess or deficiency of electrons. Besides, with some departure from half-filling an additional narrow band of quasiparticle states arises near the Fermi level. The dispersion of the band, its bandwidth and the variation with filling are close to those of the spin-polaron band of the t-J model. For moderate doping spectral intensities in the new band and in one of the inner bands of the four-band structure decrease as the Fermi level is approached which leads to the appearance of a pseudogap in the spectrum.Comment: 8 pages, 7 figure

ac Josephson effect in asymmetric superconducting quantum point contacts

We investigate ac Josephson effects between two superconductors connected by a single-mode quantum point contact, where the gap amplitudes in the two superconductors are unequal. In these systems, it was found in previous studies on the dc effects that, besides the Andreev bound-states, the continuum states can also contribute to the current. Using the quasiclassical formulation, we calculate the current-voltage characteristics for general transmission $D$ of the point contact. To emphasize bound versus continuum states, we examine in detail the low bias, ballistic (D=1) limit. It is shown that in this limit the current-voltage characteristics can be determined from the current-phase relation, if we pay particular attention to the different behaviors of these states under the bias voltage. For unequal gap configurations, the continuum states give rise to non-zero sine components. We also demonstrate that in this limit the temperature dependence of the dc component follows $\tanh(\Delta_s/2T)$, where $\Delta_s$ is the smaller gap, with the contribution coming entirely from the bound state.Comment: To appear in PR

Energy dependence of current noise in superconducting/normal metal junctions

Interference of electronic waves undergoing Andreev reflection in diffusive conductors determines the energy profile of the conductance on the scale of the Thouless energy. A similar dependence exists in the current noise, but its behavior is known only in few limiting cases. We consider a metallic diffusive wire connected to a superconducting reservoir through an interface characterized by an arbitrary distribution of channel transparencies. Within the quasiclassical theory for current fluctuations we provide a general expression for the energy dependence of the current noise.Comment: 5 pages, 1 Figur

One-dimensional conduction in Charge-Density Wave nanowires

We report a systematic study of the transport properties of coupled one-dimensional metallic chains as a function of the number of parallel chains. When the number of parallel chains is less than 2000, the transport properties show power-law behavior on temperature and voltage, characteristic for one-dimensional systems.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

NN potentials from inverse scattering in the J-matrix approach

An approximate inverse scattering method [7,8] has been used to construct separable potentials with the Laguerre form factors. As an application, we invert the phase shifts of proton-proton in the $^1S_0$ and $^3P_2-^3F_2$ channels and neutron-proton in the $^3S_1-^3D_1$ channel elastic scattering. In the latter case the deuteron wave function of a realistic $np$ potential was used as input.Comment: LaTex2e, 17 pages, 3 Postscript figures; corrected typo

Theory of thermal and charge transport in diffusive normal metal / superconductor junctions

Thermal and charge transport in the diffusive normal metal(DN) / insulator / $s$-, $d$- and p-wave superconductor junctions are studied for various situations, where we have used the Usadel equation with Nazarov's generalized boundary condition. Thermal and electrical conductance of the junction and the Lorentz ratio are calculated by varying the magnitudes of the resistance, the Thouless energy and the magnetic scattering rate in DN, the transparency of the insulating barrier, and the angle between the normal to the interface and the crystal axis of d-wave superconductors or the angle between the normal to the interface and the lobe direction of the p-wave pair potential. New general expression is derived for the calculation of the thermal conductance. It is demonstrated that the proximity effect doesn't influence the thermal conductance while the mid gap Andreev resonant states suppress it. We have also discussed a possibility of distinguishing pairing symmetries based on the dependencies of the electrical and thermal conductance on temperatures.Comment: 21 pages, 20 figures, stylistic changes in v