Interplay between single-particle and two-particle tunneling in normal metal-d-wave superconductor junctions probed by shot noise

We discuss how life-time broadening of quasiparticle states influences single- and two-particle current transport through zero-energy states at normal metal/d-wave superconductor junctions. We distinguish between intrinsic broadening (imaginary part $\eta$ of the energy), which couples the bound states with the superconducting reservoir, and broadening due to leakage through the junction barrier, which couples the bound states with the normal metal reservoir. We show that shot noise is highly sensitive to the mechanism of broadening, while the conductance is not. In the limit of small but finite intrinsic broadening, compared to the junction transparency $D$, $\eta/\Delta_0\ll D$, the low-voltage shot noise at zero frequency and zero temperature becomes proportional to the magnitude $\eta$ of intrinsic broadening ($\Delta_0$ is the maximum d-wave gap).Comment: 6 pages, 4 figures; presented at the SDP2001 conference in Toky

Proximity Effect in Normal Metal - High Tc Superconductor Contacts

We study the proximity effect in good contacts between normal metals and high Tc (d-wave) superconductors. We present theoretical results for the spatially dependent order parameter and local density of states, including effects of impurity scattering in the two sides, s-wave pairing interaction in the normal metal side (attractive or repulsive), as well as subdominant s-wave paring in the superconductor side. For the [100] orientation, a real combination d+s of the order parameters is always found. The spectral signatures of the proximity effect in the normal metal includes a suppression of the low-energy density of states and a finite energy peak structure. These features are mainly due to the impurity self-energies, which dominate over the effects of induced pair potentials. For the [110] orientation, for moderate transparencies, induction of a d+is order parameter on the superconductor side, leads to a proximity induced is order parameter also in the normal metal. The spectral signatures of this type of proximity effect are potentially useful for probing time-reversal symmetry breaking at a [110] interface.Comment: 10 pages, 10 figure

Ferromagnetic features on zero-bias conductance peaks in ferromagnet/insulator/superconductor junction

We present a formula for tunneling conductance in ballistic ferromagnet/ferromagnetic insulator/superconductor junctions where the superconducting state has opposite spin pairing symmetry. The formula can involve correctly a ferromagnetism has been induced by effective mass difference between up- and down-spin electrons. Then, this effective mass mismatch ferromagnet and standard Stoner ferromagnet have been employed in this paper. As an application of the formulation, we have studied the tunneling effect for junctions including spin-triplet p-wave superconductor. The conductace spectra show a clear difference between two ferromagnets depending upon the way of normalization of the conductance. Especially, a essential difference is seen in zero-bias conductance peaks reflecting characteristics of each ferromagnets. From obtained results, it will be suggested that the measurements of the tunneling conductance in the junction provide us a useful information about the mechanism of itinerant ferromagnetism in metal.Comment: 8 pages, 8 figures, references added to the first versio

Phase Crystals

Superconductivity owes its properties to the phase of the electron pair condensate that breaks the $U(1)$ symmetry. In the most traditional ground state, the phase is uniform and rigid. The normal state can be unstable towards special inhomogeneous superconducting states: the Abrikosov vortex state, and the Fulde-Ferrell-Larkin-Ovchinnikov state. Here we show that the phase-uniform superconducting state can go into a fundamentally different and more ordered non-uniform ground state, that we denote as a phase crystal. The new state breaks translational invariance through formation of a spatially periodic modulation of the phase, manifested by unusual superflow patterns and circulating currents, that also break time-reversal symmetry. We list the general conditions needed for realization of phase crystals. Using microscopic theory we then derive an analytic expression for the superfluid density tensor for the case of a non-uniform environment in a semi-infinite superconductor. We demonstrate how the surface quasiparticle states enter the superfluid density and identify phase crystallization as the main player in several previous numerical observations in unconventional superconductors, and predict existence of a similar phenomenon in superconductor-ferromagnetic structures. This analytic approach provides a new unifying aspect for the exploration of boundary-induced quasiparticles and collective excitations in superconductors. More generally, we trace the origin of phase crystallization to non-local properties of the gradient energy, which implies existence of similar pattern-forming instabilities in many other contexts.Comment: 8 pages, 4 figure

Dynamical effects of an unconventional current-phase relation in YBCO dc-SQUIDs

The predominant d-wave pairing symmetry in high temperature superconductors allows for a variety of current-phase relations in Josephson junctions, which is to a certain degree fabrication controlled. In this letter we report on direct experimental observations of the effects of a non-sinusoidal current-phase dependence in YBCO dc-SQUIDs, which agree with the theoretical description of the system.Comment: 4 pages, 4 ps figures, to apprear in Phys. Rev. Let

Odd-frequency pairing in normal metal/superconductor junctions

We study the induced odd-frequency pairing states in ballistic normal metal/superconductor (N/S) junctions where a superconductor has even-frequency symmetry in the bulk and a normal metal layer has an arbitrary length. Using the quasiclassical Green's function formalism, we demonstrate that, quite generally, the pair amplitude in the junction has an admixture of an odd-frequency component due to the breakdown of translational invariance near the N/S interface where the pair potential acquires spatial dependence. If a superconductor has even-parity pair potential (spin-singlet s-wave state), the odd-frequency pairing component with odd-parity is induced near the N/S interface, while in the case of odd-parity pair potential (spin-triplet $p_{x}$-wave or spin-singlet $d_{xy}$-wave) the odd-frequency component with even-parity is generated. We show that in conventional s-wave junctions, the amplitude of the odd-frequency pairing state is enhanced at energies corresponding to the peaks in the local density of states (LDOS). In $p_x$- and $d_{xy}$-wave junctions, the amplitude of the odd-frequency component on the S side of the N/S interface is enhanced at zero energy where the midgap Andreev resonant state (MARS) appears due to the sign change of the pair potential. The odd-frequency component extends into the N region and exceeds the even-frequency component at energies corresponding to the LDOS peak positions, including the MARS.Comment: 27 pages, 12 figure