Unconventional Pairing State Research Articles

Anomalous magnetic field dependence ofY Ba2Cu3O7 − δ: effect of orthorhombic distortion

In this work an attempt has been made to ascertain the originof the mixed symmetry state of the order parameters in the high-Tc superconductorY Ba2Cu3O7 − δ, with the contesting candidates being the orthorhombic distortion associated with theCuO2 planesand an s-wave order parameter component originating from the CuO chains present in thesystem. Due to its applicability over the entire range of applied magnetic fieldHc1 < H < Hc2 the present theoretical model has been employed to study various unusualproperties which are signatures of the unconventional pairing state symmetryof this material. The results presented in this paper and their agreement withthe relevant experimental data suggest that the origin of the mixed symmetrystate of pairing and the various experimentally observed unusual properties ofY Ba2Cu3O7 − δ includingthe anomalous magnetic field dependence of the vortex lattice structure, unusual upward curvature ofthe Hc2(T) plot, etc, can be attributed to the orthorhombic distortion of theCuO2 planes present in this material. However, the effect discussed in the present work pertainsto the orthorhombic distortion arising only through a second-order coupling; the distortionarising from other possible sources, namely anisotropic mixed gradient coupling, has notbeen taken into account here. Hence this discussion is restricted to a qualitativeexplanation of the effect due to orthorhombic distortion arising from the second-ordercoupling only.

Properties of Josephson junctions involving thecos(kx)⋅cos(ky)pairing state in iron pnictides

We propose a trilayer $\ensuremath{\pi}$-junction that takes advantage of the unconventional ${s}_{{x}^{2}{y}^{2}}=\text{cos}\text{ }{k}_{x}\text{ }\text{cos}\text{ }{k}_{y}$ pairing symmetry which changes sign between electron and hole Fermi pockets in the iron pnictides. In addition, we also present theoretical results for Andreev bound states in thin superconductor-normal metal (or insulator) iron-pnictide junctions. The presence of nontrivial in-gap states, which uniquely appear in this unconventional pairing state, is a distinct feature in comparison to other singlet pairing states.

Pairing symmetry and pairing state in ferropnictides: Theoretical overview

We review the main ingredients for an unconventional pairing state in the ferropnictides, with particular emphasis on interband pairing due to magnetic fluctuations. Summarizing the key experimental prerequisites for such pairing, the electronic structure and nature of magnetic excitations, we discuss the properties of the s ± state that emerges as a likely candidate pairing state for these materials and survey experimental evidence in favor of and against this novel state of matter.

Possible Pairing Symmetry of Superconductor NaxCoO2·yH2O

To discuss a possibility that the superconductivities in Na_xCoO_2yH_2O are induced by the electron correlation, we investigate the possible pairing symmetry based on the single-band Hubbard model whose dispersion of the bare energy band is obtained by using FLAPW-LDA band structure calculation of Na_xCoO_2yH_2O. The superconducting transition temperature is estimated by solving the Eliashberg equation. In this equation, both normal and anomalous self-energies are calculated up to the third-order terms with respect to the Coulomb repulsion. In the case of spin-singlet pairing, the candidate of pairing symmetry (the maximum eigen value \lambda_max^SS of Eliashberg's equation) belongs to d-wave(E_2 representation of D_6 group). In the case of spin-triplet pairing, the candidate of pairing symmetry (the maximum eigen value \lambda_max^ST of Eliashberg's equation) belongs to f_{y(y^{2}-3x^{2})}-wave (B_1 representation of D_6 group). It is found that \lambda_max^SS\simeq\lambda_max^ST and the transition temperatures of unconventional pairing state are estimated to be low compared with observed temperature within our simple model.

Impurity Site NMR Relaxation in Unconventional Superconductors

Impurity nuclear spin relaxation is studied theoretically. A single impurity generates a bound state localized around the impurity atom in unconventional superconductors. With increasing impurity potential, the relaxation rate $T_1^{-1}$ is reduced by the impurity potential. However, it has a peak at low temperatures due to the impurity bound state. The peak disappears at non-impurity sites. The impurity site NMR measurement detecting a local electronic structure just on the impurity atom is very useful for identifying the unconventional pairing states.

Current and temperature controlled variable inductance in superconducting microstrip lines

The inductance of superconducting microstrip lines is measured both as a function of current and temperature. The measurements are performed at 10 MHz for both meander and straight lines by using a multi-frequency LCR meter. The normal state resistance is observed to follow a linear temperature dependence with a slope of 3.59/spl times/10/sup -3//K for the straight line and with a slope of 2.96/spl times/10/sup -3//K for the meander line. The change in inductance is well described by a quadratic dependence on temperature. This result is consistent with an unconventional pairing state. As for the dependence on the bias current, the inductance shows a squared dependence on the bias current. The results for the current- and temperature-controlled inductance are in good agreement with an equation derived using the Ginzburg-Landau theory for the case of thin films.

Angular dependence of the penetration depth in unconventional superconductors

We examine the Meissner state nonlinear electrodynamic effects on the field and angular dependence of the low-temperature penetration depth \ensuremath{\lambda} of superconductors in several kinds of unconventional pairing states, with nodes or deep minima (``quasinodes'') in the energy gap. Our calculations are prompted by the fact that, for typical unconventional superconducting material parameters, the predicted size of these effects for \ensuremath{\lambda} exceeds the available experimental precision for this quantity by a much larger factor than for others. We obtain expressions for the nonlinear component of the penetration depth \ensuremath{\Delta}\ensuremath{\lambda} for different two- and three-dimensional nodal or quasinodal structures. Each case has a characteristic signature as to its dependence on the size and orientation of the applied magnetic field. This shows that \ensuremath{\Delta}\ensuremath{\lambda} measurements can be used to elucidate the nodal or quasinodal structure of the energy gap. For nodal lines we find that \ensuremath{\Delta}\ensuremath{\lambda} is linear in the applied field, while the dependence is quadratic for point nodes. For layered materials with ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\mathrm{\ensuremath{\delta}}}$ type anisotropy, our results for the angular dependence of \ensuremath{\Delta}\ensuremath{\lambda} differ greatly from those for tetragonal materials and are in agreement with experiment. For the two- and three-dimensional quasinodal cases, \ensuremath{\Delta}\ensuremath{\lambda} is no longer proportional to a power of the field and the field and angular dependences are not separable, with a suppression of the overall signal as the node is filled in.

Surface states and tunneling spectroscopy of high-Tcsuperconductors

Recent studies of high- Tcsuperconductors have clarified new aspects of tunneling spectroscopy. The unconventional pairing states, i.e. d-wave symmetry in these materials have been established through various measurements. Differently from isotropic s-wave superconductors, d-wave pairing states have an internal phase of the pair potential. The internal phase modifies the surface states due to the interference effect of the quasiparticles. Along these lines, a novel formula of tunneling spectroscopy has been presented that fully takes into account of the anisotropy of the pair potential. The most essential difference of this formula from conventional ones is that it suggests the phase-sensitive capability of tunneling spectroscopy. The formula suggests that the symmetry of the pair potential is determined by the orientational dependence measurements of tunneling spectroscopy. Along these lines, several experiments have been performed on high-Tc superconductors. The observation of the zero-bias conductance peaks (ZBCP) on Y Ba2Cu3O7−δstrongly suggests the dx2−y2-wave pairing states of hole-doped high-Tc superconductors. On the other hand, the absence of ZBCP on (electron-doped)Nd1.85Ce0.15CuO4−δindicates that the pair potential of this material is a nodeless state. In this paper, recent developments of tunneling spectroscopy for anisotropic superconductors are reviewed both on theoretical and experimental aspects.

Erratum

Recent studies of high- Tcsuperconductors have clarified new aspects of tunneling spectroscopy. The unconventional pairing states, i.e. d-wave symmetry in these materials have been established through various measurements. Differently from isotropic s-wave superconductors, d-wave pairing states have an internal phase of the pair potential. The internal phase modifies the surface states due to the interference effect of the quasiparticles. Along these lines, a novel formula of tunneling spectroscopy has been presented that fully takes into account of the anisotropy of the pair potential. The most essential difference of this formula from conventional ones is that it suggests the phase-sensitive capability of tunneling spectroscopy. The formula suggests that the symmetry of the pair potential is determined by the orientational dependence measurements of tunneling spectroscopy. Along these lines, several experiments have been performed on high-Tc superconductors. The observation of the zero-bias conductance peaks (ZBCP) on Y Ba2Cu3O7 − δstrongly suggests the dx2 − y2-wave pairing states of hole-doped high-Tc superconductors. On the other hand, the absence of ZBCP on (electron-doped)Nd1.85Ce0.15CuO4 − δindicates that the pair potential of this material is a nodeless state. In this paper, recent developments of tunneling spectroscopy for anisotropic superconductors are reviewed both on theoretical and experimental aspects.

Surface states and tunneling spectroscopy of high-Tcsuperconductors

Recent studies of high- Tcsuperconductors have clarified new aspects of tunneling spectroscopy. The unconventional pairing states, i.e. d-wave symmetry in these materials have been established through various measurements. Differently from isotropic s-wave superconductors, d-wave pairing states have an internal phase of the pair potential. The internal phase modifies the surface states due to the interference effect of the quasiparticles. Along these lines, a novel formula of tunneling spectroscopy has been presented that fully takes into account of the anisotropy of the pair potential. The most essential difference of this formula from conventional ones is that it suggests the phase-sensitive capability of tunneling spectroscopy. The formula suggests that the symmetry of the pair potential is determined by the orientational dependence measurements of tunneling spectroscopy. Along these lines, several experiments have been performed on high-Tc superconductors. The observation of the zero-bias conductance peaks (ZBCP) on Y Ba2Cu3O7−δstrongly suggests the dx2−y2-wave pairing states of hole-doped high-Tc superconductors. On the other hand, the absence of ZBCP on (electron-doped)Nd1.85Ce0.15CuO4−δindicates that the pair potential of this material is a nodeless state. In this paper, recent developments of tunneling spectroscopy for anisotropic superconductors are reviewed both on theoretical and experimental aspects.

Grain size dependence of the Wohlleben effect in Bi-2212 high temperature superconductors

We report on a study of the Wohlleben effect (WE) in powders of Bi-2212 high temperature superconductor (HTSC) consisting of isolated grains with dimensions ranging between 1 μm< d<1 mm. Our main results are: (i) The WE is present in all powders studied; in particular, the effect is appreciable even for grains of dimension 1 μm. (ii) The field cooled and zero field-cooled susceptibilities as well as the microwave absorption (MWA) are strongly suppressed for d<30–50 μm. (iii) In aligned powders, the WE is strongest for magnetic fields parallel to the c-axes. Our data give evidence that the WE is an intragrain property, i.e., it is not predominantly determined by intergrain weak links, and that the spontaneous currents flow within the ab-planes. Furthermore, the presence of the WE in 1 μm grains requires that the critical current density of the π-contacts which are generally involved to explain the spontaneous currents in the WE, must be of order 10 5–10 6 A/cm 2, even close to T c. Such large critical current densities are hardly achievable in conventional tunneling junctions suggesting that the π-contacts are highly transparent—eventually metallic—barriers. We argue that this result speaks strongly for an `intrinsic' nature of the π-contacts arising from an unconventional pairing state.

In-plane microwave conductivity of the single-layer cuprateTl2Ba2CuO6+δ

We have measured the in-plane microwave conductivity of nearly optimally doped single crystals ${(T}_{\mathrm{c}}$=78 K) of ${\mathrm{Tl}}_{2}{\mathrm{Ba}}_{2}{\mathrm{CuO}}_{6+\mathrm{\ensuremath{\delta}}}$ (Tl-2201) at 14.4, 24.8, and 35.9 GHz using cavity perturbation methods. At low temperatures, the in-plane penetration depth has a strong, linear temperature dependence, indicative of an unconventional pairing state with line nodes. The real part of the conductivity shows a broad, frequency-dependent peak near 30 K, similar to that seen in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ and ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}$ crystals. With tetragonal crystal symmetry and a single ${\mathrm{CuO}}_{2}$ plane per unit cell, Tl-2201 is the simplest structure so far to display these features.

Inductance measurements in thin films

We present a new inductance measurement technique using a multi-frequency LCR meter. The inductance of superconducting (YBCO) delay lines was measured both as a function of temperature and bias current. The measured temperature dependence of the change in inductance for both meander and straight lines shows a square dependence on temperature, in good agreement with an unconventional pairing state. The effective magnetic penetration depth can be determined from the theoretical expression of the inductance for the case of a microstrip configuration with two identical superconducting films. The current-controlled inductance is well described by a modified Ginzburg - Landau equation.

Ab-Plane surface impedance of the single-layer cuprate Tl 2Ba 2CuO 6+δ

The ab-plane surface impedance of Tl 2Ba 2CuO 6+δ (Tl-2201) has been measured at 14.4, 24.8 and 35.9 GHz using cavity perturbation techniques. The result of these measurements is a picture of the superconducting electrodynamics of Tl-2201 that closely resembles those of YBa 2Cu 3O 7−δ and Bi 2Sr 2CaCu 2O 8. Here we describe the main features of our measurements; in particular, we see a linear temperature dependence of the in-plane penetration depth at low temperature, consistent with an unconventional pairing state with line nodes. The simple crystal structure of Tl-2201 (tetragonal, with a single CuO 2 plane/unit cell) makes this an interesting addition to our knowledge of cuprate electrodynamics.

High-sensitivity vibrating reed studies of superconductors

Recent improvements in the vibrating reed (VR) technique permit precision studies of the mixed state of complex superconducting materials far below the upper critical magnetic field H c2. VR data for thin film, crystalline and ceramic (Ba 0.6K 0.4)BiO 3 samples demonstrate the sensitivity of the VR to microstructure and inhomogeneities, and a study of oNi 2B 2C reveals previously inaccessible vortex dynamical anomalies and minute details of a complex phase competition between magnetism and reentrant superconductivity. CeRu 2 VR data are reversible near H c2 where giant hysteresis is observed in DC magnetization data, but are hysteretic over an extended region at lower temperatures and fields, indicating vortex dynamics must be considered in testing the existence of unconventional pairing states proposed for this system.

Neutron scattering as a probe of unconventional superconductivity in YBa2Cu3O7 (invited) (abstract)

We have carried out a variety of neutron scattering experiments on the high temperature superconductor YBa2Cu3O7 which elucidate the unconventional microscopic properties of the cuprates and illustrate the power and versatility of neutron scattering as a probe of novel materials. Small angle magnetic neutron diffraction is thus far the only technique capable of revealing the structure of the vortex lattice in the cuprate superconductors in magnetic fields of several tesla. We have shown that in YBa2Cu3O7 the vortex lattice in this field range has an oblique structure when the field is applied along the c axis (perpendicular to the CuO2 layers). Recent theoretical work has attributed this unusual structure to the unconventional (d-wave) pairing state realized in the cuprates. We will also discuss the rich behavior of the vortex lattice when the field is tilted with respect to the c axis. We have used inelastic neutron scattering to elucidate the magnetic and lattice vibrational excitations in YBa2Cu3O7. Magnetic and phonon scattering were separated both by detailed calculations of phonon dynamical structure factors and by neutron polarization analysis. A novel resonant magnetic excitation at wave vector q=(π/a,π/a) and energy ℏω=40 meV appears in the superconducting state. The simplest model for this resonance relies on quasiparticle pair creation and implies a sign reversal of the energy gap function on the Fermi surface. Alternative models will also be discussed. We have also observed a strongly wave vector dependent renormalization of the energy and lifetime of a specific phonon in the superconducting state of YBa2Cu3O7. Since the phonon self-energy is sensitive to the anisotropies of the energy gap and Fermi surface via the electron–phonon interaction, our data contain important information about these parameters.

Quasi-classical theory of rough surface effects on unconventional BCS states

We present a quasi-classical theory of rough surface effects on unconventional BCS pairing states. We reinterpret and generalize the randomly rippled wall model for rough surfaces such that can describe the surface scattering ranging from the specular limit to the diffusive limit. We give a formal solution of the quasi-classical Green's function which already satisfies the boundary condition in a slab geometry. In the diffusive limit, our result correctly recovers the diffusive boundary condition for the GL equation in thep-wave state given by Ambegaokar, deGennes and Ranner. Some applications top-wave andd-wave states are discussed.

Pairing symmetry and electrodynamics of superconducting YBa2Cu3O7??, Nd1.85Ce0.15Ce0.15CuO4, and Nb

We experimentally investigate the pairing symmetry and electrodynamics of YBa2Cu3O7−δ (YBCO), Nd1.852Ce0.152CuO4 (NCCO), and Nb by examining the temperature dependence of the penetration depthλ(T) and surface resistanceR s (T) in a comparative manner. Using the measuredλ(T) andR s (T), we extract the complex conductivityσ=σ1−iσ2 for each sample, and the quasiparticle scattering timeΤ(T) for theab-plane andc-axis in YBCO. While NCCO and Nb show a strong resemblance in their electrodynamic properties, the electrodynamic properties of YBCO are very distinctive from the others. The results suggest that NCCO may have a BCSs-wave-like pairing state, while YBCO possibly has an unconventional pairing state. We compare the results on YBCO with thed-wave pairing scenario, as well as with other possible theoretical models.

C13NMR studies of the normal and superconducting states of the organic superconductor κ-(ET)2Cu[N(CN)2]Br

The authors report $^{13}\mathrm{C}$ NMR spin-lattice relaxation rates 1/${\mathit{T}}_{1}$ and Knight shifts ${\mathit{K}}_{\mathit{S}}$ in the quasi-two-dimensional organic superconductor \ensuremath{\kappa}-(ET${)}_{2}$Cu[N(CN${)}_{2}$]Br (${\mathit{T}}_{\mathit{c}}$=11.6 K), for an aligned single crystal. The normal-state behavior is reminiscent of the high-${\mathit{T}}_{\mathit{c}}$ cuprates, in which antiferromagnetic fluctuations and spin-gap behavior dominate. In the superconducting state, the data rule out the BCS electron-phonon mechanism as the source of the superconductivity, but support an unconventional pairing state with possible nodes in the gap function.

Temperature dependence of the Maki-Thompson fluctuation process in YBa 2Cu 3O 7 probed by magneto-transport measurements

The contributions of thermodynamic fluctuations of the superconducting order parameter to the normal-state magneto-conductivity tensor are investigated. An analysis of complementary measurements of the electrical resistivity, the Hall effect and the magnetoresistance at temperatures above T c in thin films of the high- T c superconductor YBa 2Cu 3O 7 provides a separation between the direct (Aslamazov-Larkin) and indirect (Maki-Thompson) fluctuation contributions. The direct contribution is not significantly affected by a possible unconventional pairing state and reveals consistent values for the coherence lengths in the ab plane, ξ ab (0) = 1.4 nm, and parallel to the c-axis, ξ c (0) = 0.15 nm, respectively. The excess Hall effect provides the most efficient way to detect the indirect fluctuation contribution, which is found to drop more rapidly towards higher temperatures than predicted for s wave pairing symmetry. An analysis of magnetoresistance measurements with proper correction for the magnetoresistance of the normal-state quasiparticles also indicates that the Maki-Thompson fluctuation process is smaller at higher temperatures than previously estimated.