Ferromagnet-superconductor proximity effect: The clean limit

We study theoretically the influence of ferromagnetic metals on a superconducting film in the clean limit. Using a self-consistent solution of the Bogoliubov--de Gennes equation for a ferromagnet-superconductor-ferromagnet double junction we calculate the pair potential and conductance spectra as a function of the superconducting layer thickness $d$ for different strengths of ferromagnets and interface transparencies. We find that the pair potential and the critical temperature are weakly perturbed by the exchange interaction and do not drop to zero for any finite $d$. On the other hand, for thin superconducting films charge transport is spin polarized and exhibits a significant dependence on the ferromagnetic strength and magnetization alignment.Comment: 5 pages, 4 figure

Spin-polarized currents in superconducting films

We present a microscopic theory of coherent quantum transport through a superconducting film between two ferromagnetic electrodes. The scattering problem is solved for the general case of ferromagnet/superconductor/ferromagnet (FSF) double-barrier junction, including the interface transparency from metallic to tunnel limit, and the Fermi velocity mismatch. Charge and spin conductance spectra of FSF junctions are calculated for parallel (P) and antiparallel (AP) alignment of the electrode magnetization. Limiting cases of nonmagnetic normal-metal electrodes (NSN) and of incoherent transport are also presented. We focus on two characteristic features of finite size and coherency: subgap tunneling of electrons, and oscillations of the differential conductance. Periodic vanishing of the Andreev reflection at the energies of geometrical resonances above the superconducting gap is a striking consequence of the quasiparticle interference. Also, the non-trivial spin-polarization of the current is found for FSF junctions in AP alignment. This is in contrast with the incoherent transport, where the unpolarized current is accompanied by excess spin accumulation and destruction of superconductivity. Application to spectroscopic measurements of the superconducting gap and the Fermi velocity is also discussed.Comment: 11 pages, 11 figure

Quasiparticle Spectrum of Vortices in Cuprates

The quasiparticle excitation spectrum of an isolated vortex in a clean layered d-wave superconductor is calculated, using both the Bogoliubov--de Gennes and the quasiclassical Eilenberger equations. Analytical solutions are obtained within the model of step-variation of the gap function, adjusting the Caroli, de Gennes and Matricon approach for low-lying excitations in cuprates. A large peak in the density of states in the "pancake" vortex core is found, caused by the two-dimensional and strong coupling nature of high-temperature superconductivity.Comment: 8 pages, Latex, uses spie1.sty, 6 eps figures, published in SPIE Proceedings, Vol. 3481 (SPIE, Bellingham, 1998), p. 106-11

Coherent effects in double-barrier ferromagnet/superconductor/ferromagnet junctions

Coherent quantum transport in ferromagnet/superconductor/ferromagnet (FSF) double-barrier junctions is studied. Analytic expressions for charge and spin conductance spectra are derived for the general case of insulating interfaces (from metallic to tunnel limit), the Fermi velocity mismatch, and for parallel (P) and antiparallel (AP) alignment of the electrode magnetizations. We focus on two characteristic features of finite size and coherency: subgap electronic transport, and oscillations of the differential conductance. Periodic vanishing of the Andreev reflection at the energies of geometrical resonances above the superconducting gap is a striking consequence of the quasiparticle interference. In contrast with the case of incoherent transport, a non-trivial spin-polarization without the excess spin accumulation is found for the AP alignment.Comment: 12 pages, 5 figure

Tutte and Jones polynomials of link families

This article contains general formulas for Tutte and Jones polynomials for families of knots and links given in Conway notation and "portraits of families"-- plots of zeroes of their corresponding Jones polynomials