Spontaneously broken translational symmetry at edges of high-temperature superconductors: thermodynamics in magnetic field

We investigate equilibrium properties, including structure of the order parameter, superflow patterns, and thermodynamics of low-temperature surface phases of layered d_{x^2-y^2}-wave superconductors in magnetic field. At zero external magnetic field, time-reversal symmetry and continuous translational symmetry along the edge are broken spontaneously in a second order phase transition at a temperature $T^*\approx 0.18 T_c$, where $T_c$ is the superconducting transition temperature. At the phase transition there is a jump in the specific heat that scales with the ratio between the edge length $D$ and layer area ${\cal A}$ as $(D\xi_0/{\cal A})\Delta C_d$, where $\Delta C_d$ is the jump in the specific heat at the d-wave superconducting transition and $\xi_0$ is the superconducting coherence length. The phase with broken symmetry is characterized by a gauge invariant superfluid momentum ${\bf p}_s$ that forms a non-trivial planar vector field with a chain of sources and sinks along the edges with a period of approximately $12\xi_0$, and saddle point disclinations in the interior. To find out the relative importance of time-reversal and translational symmetry breaking we apply an external field that breaks time-reversal symmetry explicitly. We find that the phase transition into the state with the non-trivial ${\bf p}_s$ vector field keeps its main signatures, and is still of second order. In the external field, the saddle point disclinations are pushed towards the edges, and thereby a chain of edge motifs are formed, where each motif contains a source, a sink, and a saddle point. Due to a competing paramagnetic response at the edges, the phase transition temperature $T^*$ is slowly suppressed with increasing magnetic field strength, but the phase with broken symmetry survives into the mixed state.Comment: 12 pages, 9 figure

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

Local density of states for the corner geometry interface of d-wave superconductors, within the extended Hubbard model

The spatial variations of the order parameter, and the local density of states (LDOS) on the corner of s-wave or $d_{x^2-y^2}$-wave superconductors, as well as in superconductor-insulator-normal metal interfaces, are calculated self consistently using the Bogoliubov-deGennes formalism within the two dimensional extended Hubbard model. The exact diagonalization method is used. Due to the suppression of the dominant d-wave order parameter, the extended s-wave order parameter is induced near the surface, that alternates its sign for the topmost sites at adjacent edges of the lattice and decays to zero in the bulk. The presence of surface roughness results into the appearance of the zero band conduction peak (ZBCP) near the corner surface which lacks from the predictions of the quasiclassical theory.Comment: 13 pages with 17 figure

Andreev Reflection and Spin Injection into s−s- and d−d-wave Superconductors

We study the effect of spin injection into $s-$ and $d-$wave superconductors, with an emphasis on the interplay between boundary and bulk spin transport properties. The quantities of interest include the amount of non-equilibrium magnetization ($m$), as well as the induced spin-dependent current ($I_s$) and boundary voltage ($V_s$). In general, the Andreev reflection makes each of the three quantities depend on a different combination of the boundary and bulk contributions. The situation simplifies either for half-metallic ferromagnets or in the strong barrier limit, where both $V_s$ and $m$ depend solely on the bulk spin transport/relaxation properties. The implications of our results for the on-going spin injection experiments in high $T_c$ cuprates are discussed.Comment: 4 pages, REVTEX, 1 figure included; typos correcte

Transport properties of ferromagnet/d-wave superconductor/ferromagnet double junctions

We investigate transport properties of a trilayer made of a d-wave superconductor connected to two ferromagnetic electrodes. Using Keldysh formalism we show that crossed Andreev reflection and elastic cotunneling exist also with d-wave superconductors. Their properties are controlled by the existence of zero energy states due to the anisotropy of the d-wave pair potential.Comment: 16 pages, 4 figures, revised versio

Field induced dx2−y2+idxyd_{x^2-y^2}+id_{xy} state and marginal stability of high-Tc superconductors

It is shown that the {\em complex} $d_{xy}$ component is generated in d-wave superconductor in the magnetic field. As one enters superconducting state at finite field the normal to superconducting transition occurs into bulk $d_{x^2-y^2}+i d_{xy}$ state . The driving force for the transition is the linear coupling between magnetic field and non zero magnetization of the $d_{x^2-y^2}+i d_{xy}$ condensate. The external magnetic field violates parity and time reversal symmetries and the nodal quasiparticle states respond by generating the $id_{xy}$ component of the order parameter, with the magnitude estimated to be on the order of few Kelvin. Parity (P) and time reversal (T) symmetries are violated in this state.Comment: 4 pages, latex file with two eps figure file

Mechanism of pseudogap probed by a local impurity

The response to a local strong non-magnetic impurity in the pseudogap phase is examined in two distinctly different scenarios: phase-fluctuation (PF) of pairing field and d-density-wave (DDW) order. In the PF scenario, the resonance state is generally double-peaked near the Fermi level, and is abruptly broadened by vortex fluctuations slightly above the transition temperature. In the DDW scenario, the resonance is single-peaked and remains sharp up to gradual intrinsic thermal broadening, and the resonance energy is analytically determined to be at minus of the chemical potential.Comment: 4 pages, 2 figure

Critical currents in Josephson junctions, with unconventional pairing symmetry: dx2−y2+isd_{x^2-y^2}+is versus dx2−y2+idxyd_{x^2-y^2}+id_{xy}

Phenomenological Ginzburg-Landau theory is used to calculate the possible spontaneous vortex states that may exist at corner junctions of $d_{x^2-y^2}+ix$-wave, (where $x=s$ or $x=d_{xy}$) and s-wave superconductors. We study the magnetic flux and the critical current modulation with the junction orientation angle $\theta$, the magnitude of the order parameter, and the magnetic field $H$. It is seen that the critical current $I_c$ versus the magnetic flux $\Phi$ relation is symmetric / asymmetric for $x=d_{xy}/s$ when the orientation is exactly such that the lobes of the dominant $d_{x^2-y^2}$-wave order parameter points towards the two junctions, which are at right angles for the corner junction. The conclusion is that a measurement of the $I_c(\Phi)$ relation may distinguish which symmetry ($d_{x^2-y^2}+is$ or $d_{x^2-y^2}+id_{xy}$) the order parameter has.Comment: 11 pages with 11 figures, Changed conten