Wave Order Parameter Research Articles

π-SQUIDs based on Josephson contacts between high-Tcand low-Tcsuperconductors

For phase-sensitive studies on the pairing-symmetry in a given superconductor, its combination with a well-characterized isotropic superconductor into a superconducting quantum interference device (SQUID) provides a very fruitful method. With a well-controlled orientation and position of the hybrid Josephson junctions involved, the angular dependence of both the phase and the magnitude of the order parameter wave function can be determined. In view of this, and motivated by recent proposals for quantum-logic devices, we have investigated low-inductance dc SQUIDs with different geometries. These SQUIDs are based on ramp-type YBa2Cu3O7/Au/Nb junctions oriented toward the , YBa2Cu3O7−δ crystal axes. For SQUIDs with perpendicularly oriented junctions, maxima in the critical current are observed at applied fluxes of ±1/2 Φ0 , confirming the predominant dx2-y2 pairing symmetry in YBa2Cu3O7. The measured critical current-modulations for these π-SQUIDs correspond well to simulations. No indications are found for any time-reversal symmetry breaking, for instance resulting from imaginary symmetry admixtures.

Theory of the incommensurate smectic-A phases in dimesogenic liquid crystals.

A mechanism assuming a mismatch between the basic smectic periodicity and the amplitude and phase modulations periods of the mass density wave order parameter is proposed, for describing the incommensurate smectic-A structure found in dimesogenic liquid crystals. The different sequences of phases found in this family of compounds are described theoretically.

Observation of McMillan-Rowell like oscillations in underdopedYBa2Cu3Oyjunctions oriented along the node of thed-wave order parameter

Dynamic resistance spectra of ramp junctions made of underdoped YBCO electrodes and Ga-doped YBCO barrier are reported. Series of equidistant peaks were observed in these spectra in junctions oriented along the node direction. Junctions with different barrier thickness d_N, showed that the distance between adjacent peaks scales inversely with d_N. The peaks were thus identified as due to McMillan-Rowell like oscillations in the barrier. Analysis of the series of peaks yields an upper limit of about 3.7 meV on the value of the energy gap along the node. We attribute this small gap to the complex s component of the order parameter of underdoped YBCO near the interface of the junctions.

Gossamer superconductivity in κ-(BEDT-TTF) 2X?

It has been recently established that the superconductivity (SC) in κ-(BEDT-TTF) 2Cu[N(CN) 2]Br is extremely sensitive to the cooling procedure through 100–70 K, where the ethylene groups attached to the BEDT-TTF molecules order with very slow relaxation times (the glass transition). In particular, the superconductivity in the annealed samples is described in terms of d x 2− y 2 -wave, while the quenched samples have very small (by a factor of 10 −2 or less) superfluid density with the different temperature dependence. In spite of this dramatic difference, the SC transition temperature of these samples is practically unchanged. We propose that this dramatic decrease in the superconductivity is due to the appearance of spin-density wave order parameter in the quenched samples.

Influence of surface roughness on subdominant pairing ind-wave superconductors

We study a d-wave superconductor with dominant $d_{x^2-y^2}$-wave order parameter and subdominant pairing in either the $s$- or the $d_{xy}$-wave channel near a surface. In particular we analyze the influence of surface roughness on the mixed order parameter which may break the time-reversal symmetry. We find that the subdominant component is suppressed by the roughness independent of its pairing symmetry; for very rough surfaces the subdominant component may even vanish completely. Additionally we discuss a possible real-valued admixture which counteracts the suppression of the $d_{x^2-y^2}$-wave order parameter at the surface.

Translational symmetry breaking in the superconducting state of the cuprates: Analysis of the quasiparticle density of states

Motivated by the recent STM experiments of J.E. Hoffman et.al. and C. Howald et.al., we study the effects of weak translational symmetry breaking on the quasiparticle spectrum of a d-wave superconductor. We develop a general formalism to discuss periodic charge order, as well as quasiparticle scattering off localized defects. We argue that the STM experiments in $Bi_2Sr_2CaCu_2O_{8+\delta}$ cannot be explained using a simple charge density wave order parameter, but are consistent with the presence of a periodic modulation in the electron hopping or pairing amplitude. We review the effects of randomness and pinning of the charge order and compare it to the impurity scattering of quasiparticles. We also discuss implications of weak translational symmetry breaking for ARPES experiments.

Thermodynamic properties of thed-density-wave order in cuprates

We solve a popular effective Hamiltonian of competing d-density-wave and d-wave superconductivity orders, self-consistently at the mean-field level for a wide range of doping and temperatures. The theory predicts a temperature dependence of the d-density wave order parameter seemingly inconsistent with the neutron-scattering and muon scattering resonance experiments of the cuprates. We further calculate thermodynamic quantities, such as chemical potential, entropy, and specific heat. Their distinct features can be used to test the existence of the d-density-wave order in cuprates.

Anisotropics-wave superconductivity in borocarbidesLuNi2B2CandYNi2B2C

The symmetry of superconductivity in borocarbides LuNi2B2C and YNi2B2C is an outstanding issue. Here an anisotropic s- wave order parameter (or s+g model) is proposed for these borocarbides. In spite of the dominant s- wave component the proposed superconducting order parameter has nodes and gives rise to the H^(1/2) dependent specific heat in the vortex state (the Volovik effect). This model predicts the fourfold symmetry both in the angular dependent thermal conductivity and in the excess Dingle temperature in the vortex state, which should be readily accessible experimentally.

Mixed dx2− y2+ idxy order parameters in cuprate superconductors

Taking into account the nearest-neighbor and next-nearest-neighbor attractive interactions ( V 1 and V 2), we develop a pair of coupled gap equation for the mixed ( d x 2− y 2 + id xy )-wave order parameter in the van Hove scenario. It is found that d xy component of the order parameter increases linearly with V 2/ V 1. For a fixed V 2/ V 1 there is a characteristic temperature T ∗ below the critical superconducting temperature T c . At T<T ∗ the d x 2− y 2 - and d xy -waves coexist, while for T ∗<T<T c only the d x 2− y 2 -wave pairing exists.

Odd-frequency density waves: Non-Fermi-liquid metals with an order parameter

We consider states with a charge- or spin-density wave order parameter which is odd in frequency so that the order parameter vanishes at zero frequency and there is a conventional Fermi surface. Such states break translational symmetry and, therefore, are not conventional Fermi liquids. In the odd-frequency spin-density wave case, there are Goldstone bosons and the low-energy spectrum is manifestly different from that of a Fermi liquid. We discuss a simple model that gives rise to such ordered states. The frequency dependence of the gap leads to an unusual temperature dependence for various thermodynamic and transport properties, notably the resistivity.

Critical currents in Josephson junctions with unconventional pairing symmetry:dx2−y2+isversusdx2−y2+idxy

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.

Mixed order parameter superconducting states for different filling and temperature

We study the gap equation for the time reversal symmetry breaking states d x 2− y 2 +is and d x 2− y 2 +id xy using a tight-binding model that includes orthorhombic distortion and second- nearest-neighbor hopping, γ, at different temperatures and fillings. Mixing occurs both in square lattice and in the presence of orthorhombic distortion and also for various values of γ when studied as a function of the filling. Unlike the d x 2− y 2 +id xy case the temperature dependence of the d x 2− y 2 +is state shows a suppression in the d wave order parameter in the presence of s wave.

Competition Between Two Ordering Processes inTwo-Dimensional Doped Antiferromagnets

We provide a Landau theory of the coupledcharge density wave and spin density wave order parameters to investigatethe possibility of coexistence or competition between the two orderingprocesses occurring in the two-dimensional doped antiferromagnet. We findthat the two ordering processes can coexist only in a certain region ofcoupling parameters, and the one with lower transition temperature canonly coexist together with the other one with higher transitiontemperature and cannot be stabilized separately. Phase diagrams indifferent situations are given.

Vortex state of ad-wave superconductor at low temperatures

A systematic perturbation theory is developed to describe the magnetic field-induced subdominant $s$- and $d_{xy}$-wave order parameters in the mixed state of a $d_{x^2-y^2}$-wave superconductor, enabling us to obtain, within weak-coupling BCS theory, analytic results for the free energy of a d-wave superconductor in an applied magnetic field $H_{c1}\ltsim H\ll H_{c2}$ from $T_c$ down to very low temperatures. Known results for a single isolated vortex in the Ginzburg-Landau regime are recovered, and the behavior at low temperatures for the subdominant component is shown to be qualitatively different. In the case of subdominant $d_{xy}$ pair component, superfluid velocity gradients and an orbital Zeeman effect are shown to compete in determining the vortex state, but for realistic field strengths the latter appears to be irrelevant. On this basis, we argue that recent predictions of a low-temperature phase transition in connection with recent thermal conductivity measurements are unlikely to be correct.

Reformulation of Bogoliubov–de Gennes equations for a d-wave superconductor

By considering a pure d xy -wave order parameter (OP), the Bogoliubov–de Gennes equations for a pure d xy -wave superconductor is reformulated into a full differential form. We also derive the self-consistent equation for the OP, which is tested by the bulk state and the surface problem. Very importantly, it is shown that the new set of equations has a constrained gauge invariance.

Influence of incommensurability on SDW and CDW amplitudes in underdoped cuprates

Self-consistent calculations of spin (charge) density wave order (SDW/CDW) parameters have been performed for bilayered cuprates on the basis of a singlet correlated band model. The smooth development of the pseudogap formation temperature is explained from underdoped to overdoped states and the Fourier amplitudes < s q > (spin) and < e q > (charge) modulations have been calculated. We have found a maximum of the incommensurability for doping 0.09 ÷ 0.11 holes per copper site.

Collective mode in a superconductor with mixed-symmetry order parameter components

We consider a superconducting state with mixed-symmetry order parameter components, e.g., d+is or d+id(') with d(') = d(xy). We argue for the existence of a new orbital magnetization mode which corresponds to oscillations of relative phase straight phi between two components around an equilibrium value of straight phi = pi / 2. It is similar to the "clapping" mode in superfluid 3He-A. We estimate the frequency of this mode omega(0)(B,T) depending on the field and temperature for the specific case of magnetic field induced d(') = d(xy) state. This mode is tunable with a magnetic field with omega(0)(B,T) approximately BDelta(0), where Delta(0) is the magnitude of the d-wave order parameter. We also estimate the velocity s(B,T) of this mode.

Suppression of superconductivity in high- cuprates due to nonmagnetic impurities: Implications for the order parameter symmetry

We studied the effects of nonmagnetic impurities on high-temperature superconductors by solving the Bogoliubov-de Gennes equations on a two-dimensional lattice via exact diagonalization technique in a fully self-consistent way. We found that s-wave order parameter is almost unaffected by impurities at low concentrations while $d_{x^2-y^2}$-wave order parameter exhibits a strong linear decrease with impurity concentration. We evaluated the critical impurity concentration $n_i^c$ at which superconductivity ceases to be 0.1 which is in good agreement with experimental values. We also investigated how the orthorhombic nature of the crystal structure affects the suppression of superconductivity and found that anisotropy induces an additional s-wave component. Our results support $d_{x^2-y^2}$-wave symmetry for tetragonal and $s+d_{x^2-y^2}$-wave symmetry for orthorhombic structure.

Effect of non-magnetic impurity in superconducting states of t–J model

Abstract The effect of non-magnetic impurities in the superconducting state of the t – J model is studied. The Bogoliubov de Gennes equation is derived via a slave-boson mean-field approximation, and we solve it numerically at T =0. The d x 2 − y 2 -wave order parameter is suppressed near an impurity and the extended s-wave component is induced. The local charge density wave (CDW)-like feature due to the Friedel oscillations is found, which leads to the splitting of the expected zero-energy Andreev bound state. Therefore, an instability towards a state breaking locally time reversal symmetry or exhibiting antiferromagnetic order is unlikely to occur.

Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+delta} c-axis twist Josephson junctions : a new phase-sensitive test of order parameter symmetry.

Li et al. found that the critical current density J{sub c}{sup J} across atomically clean c-axis twist junctions of Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} is the same as that of the constituent single crystal, J{sub c}{sup S}, independent of the twist angle {phi}{sub 0}, even at and below T{sub c}. They investigated theoretically if a d{sub x{sup 2}{minus}y{sup 2}} wave order parameter might twist by mixing in d{sub xy}-wave components, but found that such mixing cannot possibly explain the data near to T{sub c}. Combined with group theoretical arguments, they then conclude that the order parameter contains at least a substantial s-wave component, but does not contain any purported d{sub x{sup 2}{minus}y{sup 2}}-wave component, except possibly below a second, unobserved phase transition. By studying tunneling models, they further conclude that the intrinsic c-axis Josephson tunneling in Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} is likely to be mostly incoherent.