Time-reversal State Research Articles

Critical currents in Josephson junctions with d+i s symmetry

The magnetic interference pattern and the spontaneous flux in unconventional Josephson junctions of superconductors with d+i s symmetry are calculated for different reduced junction lengths. The asymmetry in the field-modulated diffraction pattern exists for lengths as long as L=10 λ J. This is a time-reversal broken symmetry state. We present the evolution of the overlap critical current as a function of the crystal orientation for the fractional vortex and antivortex that are spontaneously formed near the junction center.

Magnetic interference patterns in Josephson junctions withd+issymmetry

The magnetic interference pattern and the spontaneous flux in unconventional Josephson junctions of superconductors with $d+is$ symmetry are calculated for different reduced junction lengths and the relative factor of the d- and s-wave components. This is a time-reversal broken symmetry state. We study the stability of the fractional vortex and antivortex which are spontaneously formed and examine their evolution as we change the length and the relative factor of d- and s-wave components. Asymmetry in the field-modulated diffraction pattern exists for lengths as long as $L=10{\ensuremath{\lambda}}_{J}.$

Pairing in finite systems: nuclei and fullerenes

The role the exchange of phonons between pairs of fermions moving in time reversal states lying close to the Fermi energy on the superfluidity and on the superconductivity of atomic nuclei and fullerenes respectively is discussed in terms of mean field theory and of ab-initio calculations.

Magnetic impurities ind-wave superconductors

We solve the problem of a magnetic impurity in a $d_{x^2-y^2}$-wave superconductor by a variational method. A moment is found to exist in the superconducting state only if the Kondo-temperature in the normal state is larger than the maximum in the superconducting gap-function. If a moment exists in the superconducting state, and provided spin-orbit coupling is non-zero, it induces a time-reversal breaking superconducting state locally around the inpurity which is a linear combination of the $d_{x^2-y^2}$ and $d_{xy}$ states. The current pattern around the impurity in this state are evaluated.

Spin-Triplet Superconductivity with Line Nodes in Sr2RuO4

Several possible odd-parity states are listed up group-theoretically and examined in light of recent experiments on Sr$_2$RuO$_4$. Those include some of the $f$-wave pairing states, ${\mib d}({\mib k})\propto{\hat{\mib z}} k_xk_y(k_x + {\rm i}k_y)$ and ${\hat{\mib z}} (k_x^2-k_y^2)(k_x + {\rm i}k_y)$ and other ${\hat{\mib z}} (k_x + {\rm i}k_y)\cos ck_z$ ($c$ is the $c$-axis lattice constant) as most plausible candidates. These are time-reversal symmetry broken states and have line nodes running either vertically (the former two) or horizontally (the latter), consistent with experiments. Characterizations of these states and other possibilities are given.

Surface Vibrations and the Pairing Interaction in Nuclei

The induced pairing interaction arising from the exchange of low-lying collective surface vibrations among nucleons moving in time reversal states close to a Fermi energy is found to lead to values of the pairing gap which constitute a large fraction of those experimentally observed.

Theory of tunneling effect and Josephson effect in anisotropic superconductors under spatially varying pair potentials

The influences of the spatial variation of the pair potential on the tunneling conductance in a normal metal/insulator/anisotropic superconductor (N/I/d) junction and on the Josephson effect in anisotropic superconductors are studied. The temperature dependence of the Josephson current in a d-wave superconductor/insulator/d-wave superconductor (d/I/d) junction is shown to be largely influenced by the existence of the broken time-reversal state and the roughness at the interfaces.

Tunneling into high temperature superconductors: Andreev bound states and broken time-reversal symmetry

Tunneling into high-temperature superconductors is shown to be a powerful spectroscopic probe of the unconventional superconducting state in YBa 2Cu 3O 7 (YBCO). Planar tunneling is performed on low-leakage, ab-oriented YBCO/I/Cu junctions, where I is formed with a self-assembled organic monolayer. The reproducible dependence of the tunneling conductance on temperature, magnetic-field, doping and ion-induced disorder confirm that the zero-bias conductance peak (ZBCP) is an Andreev bound state, which arises directly from a d-wave order parameter. At temperatures below ∼8 K in zero applied magnetic field, the ZBCP splits, signifying a phase transition into a broken time-reversal symmetry state. An applied magnetic field induces further splitting that grows nonlinearly with increasing field. A theoretical model that invokes the formation of sub-dominant order parameter near the surface shows striking qualitative and quantitative agreement with our data.

Time-reversal symmetry-breaking states near grain boundaries betweend-wave superconductors

In this paper we study the order parameter and density of states near a grain boundary between two ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ superconductors. We examine broken time-reversal symmetry near the interface. In particular we show that, under suitable circumstances, time-reversal symmetry must be broken even when the order parameter is purely ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ everywhere in space.

Quasiclassical Theory of Twin Boundaries in High-TcSuperconductors

We investigate the electronic structure of twin boundaries in orthorhombically distorted high-T$_c$ materials using the quasiclassical theory of superconductivity. At low temperatures we find a local instability to a time-reversal symmetry breaking state at the twin boundary. This state yields spontaneous currents along the twin boundary that are microscopically explained by the structure of the quasiparticle bound states. We calculate the local density of states and find a splitting in the zero-bias peak once the spontaneous currents set in. This splitting is measurable by STM techniques and is a unique signature of time-reversal breaking states at a twin boundary.

Influence of an isolated magnetic impurity on an unconventional superconducting state

The effect of the moment of a magnetic impurity on the order parameter of an unconventional superconductor is examined. The coupling of the magnetic moment to the order parameter induces a locally time-reversal symmetry-breaking state which generates a magnetic field distribution in the vicinity of the impurity. The magnetic field can cause precession of the magnetic moment. The case of a spin polarized muon injected into the superconductor is discussed.

Time-Reversal Symmetry Breaking at Grain Boundaries in d-Wave Superconductors

Crystal lattice distortion can generate a superconducting state which breaks locally time-reversal symmetry by yielding a coupling between order parameters of different symmetry. The problem of a twist in the crystal lattice at a boundary between differently oriented grains is investigated by means of a generalized Ginzburg–Landau theory. It is shown that under certain conditions a time-reversal breaking state appears at the grain boundary. This state leads to a nontrivial phase shift in the Josephson effect across the grain boundary. This phase shift can be observed through a modified flux quantization (fractional fluxes) and phase slip effects.

Penetration depth measurements as a test for time-reversal breaking states in unconventional superconductors

We examine the possibility of nonmagnetic impurity-induced time-reversal breaking in unconventional superconductors. We determine the phase diagram for impurity-induced broken-T-symmetry states, in a model in which a dominant unconventional order parameter is present along with a subdominant conventional one. We find that, under such conditions, a time-reversal breaking state is always possible in a wide range of impurity concentrations at sufficiently small temperatures. We determine the effect that the transition into such a phase has on the temperature dependence of the penetration depth. Our results suggest that such bulk, broken T-symmetry states could be detected by penetration depth measurements in very dirty samples.

Josephson tunneling in high-Tc superconductors.

In this article a macroscopic invariance group describing the superconducting state of a twinned crystal is introduced and shown to provide a useful framework for the discussion of Josephson tunneling in twinned crystals. Josephson tunneling from time-reversal symmetry-breaking states is described and compared with that from time-reversal invariant states for both twinned and untwinned crystals and for both c-axis and basal-plane currents, in a model for orthorhombic Y-Ba-Cu-O. In addition, a ring geometry, which allows s-wave and ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave superconductivity in a tetragonal superconductor to be distinguished on the basis of symmetry arguments only, is proposed and analyzed. Finally, an appendix gives details of the experimental Josephson tunneling evidence for a superconducting state of orthorhombic ${\mathit{ux}}^{2}$+${\mathit{vy}}^{2}$ symmetry in Y-Ba-Cu-O. \textcopyright{} 1996 The American Physical Society.

Ginzburg-Landau equations for a d-wave superconductor with applications to vortex structure and surface problems.

The properties of a {ital d}{sub {ital x}}{sup 2}{minus}{ital y}{sup 2}-wave superconductor in an external magnetic field are investigated on the basis of Gorkov`s theory of weakly coupled superconductors. The Ginzburg-Landau (GL) equations, which govern the spatial variations of the order parameter and the supercurrent, are microscopically derived. The single vortex structure and surface problems in such a superconductor are studied using these equations. It is shown that the {ital d}-wave vortex structure is very different from the conventional {ital s}-wave vortex: the {ital s}-wave and {ital d}-wave components, with the opposite winding numbers, are found to coexist in the region near the vortex core. The supercurrent and local magnetic field around the vortex are calculated. Far away from the vortex core, both of them exhibit a fourfold symmetry, in contrast to an {ital s}-wave superconductor. The surface problem in a {ital d}-wave superconductor is also studied by solving the GL equations. The total order parameter near the surface is always a {ital real} combination of {ital s}- and {ital d}-wave components, which means that the proximity effect cannot induce a time-reversal symmetry-breaking state at the surface.

SPINORS, THE DIRAC FORMALISM AND CORRECT COMPLEX CONJUGATION

It is pointed out that in the Dirac formalism ψ†γ0ψ is not a correct spinorial expression and should be replaced by [Formula: see text] where C0 is a Lorentz-invariant quantity with different spinorial indices than γ0. Although [Formula: see text] has the same matrix value as γ0 in flat space-time, the two quantities are different in curved space-time. However, γ0 retains its role as the time component of a 4-vector, and as a factor in the parity and time reversal states.

Spontaneously symmetry-broken-current-carrying states in a strongly inhomogeneous interacting two-dimensional Fermi liquid.

We examine the nature of the ground state of a two-dimensional interacting electron gas in a self-induced gauge field. We show that for a realistic form of such a many-body gauge field in two dimensions and increasing inhomogeneity of the electron density, a spontaneous current-carrying state develops. Its relation to other time-reversal broken-symmetry ground states is discussed.

Enforced Time-Reversal Breakdownin Unconventional Superconductors

In time-reversal symmetric unconventional superconductors time-reversal breaking structures can occur under certain conditions. This effect is demonstrated on two examples: a domain wall and a thin film for a superconductor with an order parameter consisting of two components. It is shown that the occurrence of time-reversal breaking states is compatible with the general stability conditions of a Ginzburg-Landau theory.