Renormalization Group Study of the Electron-phonon Interaction in the High Tc Cuprates

We generalize the numerical renormalization group scheme to study the phonon-mediated retarded interactions in the high Tc cuprates. We find that three sets of phonon-mediated retarded quasiparticle scatterings grow under RG flow. These scatterings share the following common features: 1) the initial and final quasiparticle momenta are in the antinodal regions, and 2) the scattering amplitudes have a $x^2-y^2$ symmetry. All three sets of retarded interaction are driven to strong coupling by the magnetic fluctuations around $(\pi,\pi)$. After growing strong, these retarded interaction will trigger density wave orders with d-wave symmetry. However, due to the d-wave form factor they will leave the nodal quasiparticle unaffected. We conclude that the main effect of electron-phonon coupling in the cuprates is to promote these density wave orders.Comment: 4 pages, 3 figures, references added, added more details about others' previous studie

Spin-polarized quasiparticle transport in cuprate superconductors

The effects of spin-polarized quasiparticle transport in superconducting YBa2Cu3O7-delta (YBCO) epitaxial films are investigated by means of current injection into perovskite ferromagnet-insulator-superconductor (F-I-S) heterostructures. These effects are compared with the injection of simple quasiparticles into control samples of perovskite nonmagnetic metal-insulator-superconductor (N-I-S). Systematic studies of the critical current density (J(c)) as a function of the injection current density (J(inj)), temperature (T), and the thickness (d) of the superconductor reveal drastic differences between the F-I-S and N-I-S heterostructures, with strong suppression of J(c) and a rapidly increasing characteristic transport length near the superconducting transition temperature T-c only in the F-I-S samples. The temperature dependence of the efficiency (etaequivalent toDeltaJ(c)/J(inj); DeltaJ(c): the suppression of critical current due to finite J(inj)) in the F-I-S samples is also in sharp contrast to that in the N-I-S samples, suggesting significant redistribution of quasiparticles in F-I-S due to the longer lifetime of spin-polarized quasiparticles. Application of conventional theory for nonequilibrium superconductivity to these data further reveal that a substantial chemical potential shift mu(*) in F-I-S samples must be invoked to account for the experimental observation, whereas no discernible chemical potential shift exists in the N-I-S samples, suggesting strong effects of spin-polarized quasiparticles on cuprate superconductivity. The characteristic times estimated from our studies are suggestive of anisotropic spin relaxation processes, possibly with spin-orbit interaction dominating the c-axis spin transport and exchange interaction prevailing within the CuO2 planes. Several alternative scenarios attempted to account for the suppression of critical currents in F-I-S samples are also critically examined, and are found to be neither compatible with experimental data nor with the established theory of nonequilibrium superconductivity

Superconducting proximity effect and Majorana fermions at the surface of a topological insulator

We study the proximity effect between an s-wave superconductor and the surface states of a strong topological insulator. The resulting two dimensional state resembles a spinless p_x+ip_y superconductor, but does not break time reversal symmetry. This state supports Majorana bound states at vortices. We show that linear junctions between superconductors mediated by the topological insulator form a non chiral 1 dimensional wire for Majorana fermions, and that circuits formed from these junctions provide a method for creating, manipulating and fusing Majorana bound states.Comment: 4 pages, 3 figures, published versio