High Frequency Sound in Superfluid 3He-B

We present measurements of the absolute phase velocity of transverse and longitudinal sound in superfluid ³He-B at low temperature, extending from the imaginary squashing mode to near pair-breaking. Changes in the transverse phase velocity near pair-breaking have been explained in terms of an order parameter collective mode that arises from f-wave pairing interactions, the so-called J=4^? mode. Using these measurements, we establish lower bounds on the energy gap in the B-phase. Measurement of attenuation of longitudinal sound at low temperature and energies far above the pair-breaking threshold, are in agreement with the lower bounds set on pair-breaking. Finally, we discuss our estimations for the strength of the f-wave pairing interactions and the Fermi liquid parameter, F ₄ ^s .     

Anisotropic attenuation of zero sound in superfluid3He-A

The anisotropic attenuation of zero sound in superfluid³He-A at 29.3 bar pressure has been measured at 24.4, 34.2, 44.2, 54.0, 63.9, 73.7, 83.5, and 93.4 MHz. The clapping mode resonance has been observed at all frequencies, and the reentrant normal flapping resonance has been measured for the first time. Analysis of these results leads to anf-wave pairing parameter,x ₃ ^–1 –0.1±0.05, and a determination of strong coupling corrections to the energy gap far fromT _c. This is expressed by an enhancement of the zero-temperature energy gap by a factor 1.3±0.1 above that of weak coupling, 2.03k _B T _c . The clapping mode data is consistent with a nontrivial, strong coupling correction to the mode frequency, reducing it by 6%. The³He was confined to a slab 250 µm in thickness and the superfluid texture was oriented by a magnetic field. This allowed attenuations up to 100 cm^–1 to be resolved and the attenuation from pair-breaking processes alone to be determined for the first time. The sound attenuation was measured for angles between the sound propagation direction and the1vector of 0, /4, and /2. The sensitivity of the numerically evaluated attenuation to quasiparticle collision time,f-wave parameter, and uniformity of the orbital texture is explored.     

Acoustic attenuation in superfluid3He-B at low pressures

The attenuation of zero sound in superfluid³He-B has been measured up to 160 cm^–1, at pressures less than 4 bar and at frequencies 34.2, 44.2, and 54.0 MHz. The contribution of pair breaking to the attenuation has been measured for the first time. The gap (J=1 ^–) mode has been studied in magnetic fields up to 80 mT and the structure of its Zeeman components revealed. Coupling to the gap mode in the applied field allows a direct spectroscopic measurement of the energy gap. In zero magnetic field, the attenuation is well described by the theory of Wölfle, showing agreement with the magnitude of the attenuation and the frequency of the squashing mode resonance, for an appropriate choice of the parameterz=(c ₀–c₁)/c₁, wherec ₀, c₁ are the velocities of zero and first sound. This provides a determination of the Landau parameterF ₂ ^s and indicates that thef-wave interaction is negligible at these low pressures.     

Transport Properties of Topological Insulator-Based Ferromagnet/f-Wave Superconductor Junction

We investigate effect of magnetically-induced relativistic mass and also anisotropic f-wave pair coupling on the tunneling conductance on the surface of a 3D topological insulator ferromagnet/superconductor junction, which two types of pairing for superconductivity are possible. A topological insulator as a new state of condensed-matter caused by spin–orbit interaction and time-reversal symmetry has a bulk band gap and gapless surface states. We use the BTK formalism to find the charge carriers behavior. Due to two different nature of order parameters of the f-wave superconductivity, the tunneling conductance is found to be linearly dependent on the magnetic gap in terms of f ₁ and the exponential for f ₂. It is shown that the conversion of the conductance peak from ZBCP to ZBCD occurs in the f ₁ case with increasing m, while this is not observed in f ₂. Also, we find that the conductance behaves as a unit step function for the superconductor electrostatic potential in f ₁, and this should be usable in nanoelectronic switch devices. In addition, we illustrate how the magnetic gap affects the transmission coefficient in quite different behaviors for order parameters.     

Non-linear Localized Lattice Mode Coupling Mechanism and the Pseudogap in High-temperature Superconducting Cuprates

The pseudo-gap phenomena in high-temperature cuprate superconductors is an outstanding puzzle with no consensus yet on its physical origin. A previous suggestion on the role of non-linear local lattice instability modes on the microscopic pairing mechanism in high temperature cuprate superconductors is re-examined to investigate whether unusual lattice mechanisms could cause a pseudo-gap. By assuming an electron predominantly interacting with a non-linear Q ₂ mode of the oxygen clusters in the CuO₂ planes, we show that the interaction has explicit d-wave symmetry and leads to an indirect coupling of d-wave symmetry between electrons. We show that the polaron formation by the non-linear mode can cause a pseudo-gap of d-wave symmetry before the onset of coherence in the superconducting pairing. We suggest a simple phenomenological explanation of the pseudo-gap crossover temperature and the Fermi arcs. The discussion may be relevant for the pseudo-gap in non-superconducting giant magnetoresistive manganites.     

Charge Transport in Unconventional Superconductor Junctions

We report two remarkable recent topics about zero-bias conductance peak (ZBCP) in normal-metal/unconventional superconductor junctions. We show that the roughness at a surface of superconductors strongly suppresses the ZBCP when the transparency of the interface is sufficiently low. In a numerical simulation at a zero-magnetic field, we confirm the split of the ZBCP owing to the interfacial roughness in realistic band structures of the high-T _c superconductors. We also study the influence of a magnetic field H on the zero bias conductance peak (ZBCP). For p-wave junctions, ZBCP does not split into two by H even for sufficiently low transparent junctions, where ZBCP clearly splits for d-wave. This unique property originates from the fact that for p-wave superconductors, perpendicularly injected quasiparticle form ZES, which contributes most dominantly on the tunneling conductance. We propose that tunneling spectroscopy in the presence of magnetic field, i.e., magnetotunneling, is a promising method to determine the pairing symmetry of unconventional superconductors.     

Effect of pair-breaking on the superconducting fluctuation contribution to the NMR relaxation rate

We investigate the effect of pair-breaking on the contribution of s-wave order parameter fluctuations to the NMR relaxation rate for clean 2D superconductors. For Gaussian fluctuations we evaluate the Maki-Thomson diagram taking into account pairing breaking in both the fluctuation propagator and the Green's functions. The fluctuation peak in 1/T ₁ near T_c is strongly reduced by pair-breaking as is the case for the Hebel-Slichter peak.     

Thermodynamic Functions for Superfluid Fermions in Two Dimensions

The parameters of state for interacting ultracold fermionic atoms with s-wave pairing in 2D are calculated as a function of temperature in the superfluid, pseudogap and normal states. The pseudogap pairing temperature is determined within the Gaussian pair fluctuation approach accounting for both phase and amplitude fluctuations. The thermodynamic functions vary continuously at T _BKT , whereas they can substantially change at the crossover between the pseudogap and normal states.     

Spin dynamics and implications for superconductivity: some problems with thed-wave scenario

We review the spin dynamics of the normal state of the cuprates with special emphasis on neutron data in both the YBa₂Cu₃O_7– and La_2–x Sr _x CuO₄ systems. When realistic models of the Fermi surface shapes are incorporated, along with a moderate degree of spin fluctuations, we find good semiquantitative agreement with experiment for both cuprates. Building on the success of this Fermi-liquid-based scheme, we explore the implications ford-wave pairing from a number of vantage points. We conclude that our present experimental and theoretical understanding is inadequate to confirm or refute thed-wave scenario.     

Superflow and the depairing critical current for spin singlet-triplet states of superfluid Fermi liquid

The unitary states of superfluid Fermi liquid with singlet D and triplet P type of pairing are investigated in the framework of the weak coupling approximation. The superflow pair-breaking critical current is calculated at zero temperature and in the Ginzburg-Landau region for various values of the respective strengths of singlet and triplet components of the pairing interaction. The dependence of the mass superflow on the a ₁ (F ₁ ^s ) Landau amplitude is determined. The mixed singlet-triplet states BS (a mixture of BW anisotropic and D-wave states) and 2DS (a mixture of 2D planar and D-wave states) are found to be stable for some region of the superfluid velocity.     

Anisotropic superconductivity in the Emery model

We have investigated anisotropic superconductivity originating from intersite pairing between holes in nearest and next nearest neighboring sites in the Emery model. Strong local Coulomb correlations among holes in copper orbitals have been taken into account within the Hubbard I approximation scheme. The superconducting transition temperature has been evaluated as a function of the hole concentration. It has been shown that with the onset of superconductivity, pairing among oxygen-like quasiparticles in the mixeds-wave+d-wave channel plays the dominating role, being replaced by pairing in the extendeds-wave channel for higher concentration of holes. Superconducting correlations are mostly effective for a rather narrow range of the model parameter values, close to values derived from band structure calculations. Therefore, the coupling betweens-wave andd-wave channels seems to be a general feature of superconductivity in CuO₂ planes.     

Cuprates and Ruthenates: Similarities and Differences

There is growing evidence that the p-wave superconductivity of Sr₂RuO₄ occurs primarily in the planar -band. Thus the minimum model for both cuprates and ruthenates is a single active band with onsite Coulomb interactions. Recent renormalization group analysis shows that such a model can show singlet d-wave or triplet p-wave pairing. The energy of the van Hove singularity in the band and the shape of the Fermi surface are the decisive factors at weak to moderate interaction strengths.     

Hall Coefficient of Equilibrium Supercurrents Flowing inside Superconductors

We study augmented quasiclassical equations of superconductivity with the Lorentz force, which is missing from the standard Ginzburg–Landau and Eilenberger equations. It is shown that the magnetic Lorentz force on equilibrium supercurrents induces a finite charge distribution and the resulting electric field to balance the Lorentz force. An analytic expression is obtained for the corresponding Hall coefficient of clean type-II superconductors with simultaneously incorporating the Fermi-surface and gap anisotropies. It has the same sign and magnitude at zero temperature as the normal state for an arbitrary pairing, having no temperature dependence specifically for s-wave pairing. The gap anisotropy may bring about a considerable temperature dependence in the Hall coefficient and can lead to its sign change as a function of temperature, as exemplified for a model d-wave pairing with a two-dimensional Fermi surface. The sign change may be observed in some high-T _c superconductors.     

Probing the Superconducting Pairing Symmetry from Spin Excitations in BiS2 Based Superconductors

Starting from a two-orbital model and based on the random phase approximation, spin excitations in the superconducting state of the newly discovered BiS₂ superconductors with three possible pairing symmetries are studied theoretically. It is found that the spin response is uniquely determined by the pairing symmetry. Possible spin resonance excitations may occur at an incommensurate momentum about (0.7π,0.7π) for the d-wave symmetry, while the transverse spin excitation near (0,0) is enhanced for the p-wave symmetry and no spin resonance signature is seen for the s-wave pairing symmetry. These distinct features may be used for probing or determining the pairing symmetry in this newly discovered compound.     

Collective modes and a theory of response ofd-wave superconductors

We present a theory of the response ofd-wave superconductors to weak applied fields, by taking account of the Coulomb interaction and all the collective degrees of freedom as well as crystal symmetry. We choose two representative phases: the d phase, which has point nodes in the energy gap, and theY _2–1 phase, which has line as well as point nodes. The former is a self-consistent solution for cubic as well as spherical symmetries and the latter is one for spherical, cubic, and hexagonal symmetries. We obtain obviously gauge-invariant expressions for the order-parameter fluctuations and the currents, having forms common not only to thed-wave states, but also to thep-wave states studied earlier. We also investigate the collective excitations; in the long-wavelength limit for spherically symmetric systems, there are, on the frequency-temperature plane, seven branches for eachd-wave phase considered, in addition to the common plasma mode and orbital Goldstone modes resulting from the spontaneous breakdown of the rotational invariance. In theY _2–1-phase two eigenmodes are found to become gapless at a finite temperature, below which they are purely imaginary. This implies instability of the phase. The effect of crystal anisotropy on the collective spectra is also studied.A preliminary report on the present work was published inJpn. J. Appl. Phys. Suppl. 26-3, 167 (1987).     

Spin dynamics and implications for superconductivity: some problems with thed-wave scenario

We review the spin dynamics of the normal state of the cuprates with special emphasis on neutron data in both the YBa₂Cu₃O_7?δ and La_2?x Sr _x CuO₄ systems. When realistic models of the Fermi surface shapes are incorporated, along with a moderate degree of spin fluctuations, we find good semiquantitative agreement with experiment for both cuprates. Building on the success of this Fermi-liquid-based scheme, we explore the implications ford-wave pairing from a number of vantage points. We conclude that our present experimental and theoretical understanding is inadequate to confirm or refute thed-wave scenario.     

Use of tricrystal junctions to probe the pairing state symmetry of YBa2Cu3O7

We have developed a new method of probing superconducting pairing state symmetry, by using tricrystal devices analogous tos-d corner junctions. Two central peaks are observed in the field-modulated critical currents of frustrated YBCO tricrystal junctions operating in the short junction limit, consistent with predominantly — wave pairing symmetry with little or no imaginarys-wave component. However, our results are consistent with a real combination of larged-wave and smalls-wave components. A single peak is also observed for frustrated tricrystal junctions operating in the long junction limit, and it is shown theoretically that the behaviors ofs- andd-wave superconductors are indistinguishable in this limit.     

Interplay Between Vorticity and Chirality Inside the Vortex Core in Chiral p-Wave Superconductors

The vortex core in chiral p-wave superconductors exhibits various properties owing to the interplay between the vorticity and chirality inside the vortex core. In the chiral p-wave superconductors, the site-selective nuclear spin-lattice relaxation rate T ^–1 ₁ is theoretically studied inside the vortex core within the framework of the quasiclassical theory of superconductivity. T ^–1 ₁ at the vortex center depends on the sense of the chirality relative to the sense of the magnetic field. The effect of a tilt of the magnetic field upon T ^–1 ₁ is investigated. The effect of the anisotropy in the superconducting gap and the Fermi surface is then investigated. The result is expected to be experimentally observed as a sign of the chiral pairing state in a superconducting material Sr₂RuO₄.     

Effects of phonons and antiferromagnetic spin fluctuations on the pairing and density of states in high-T c superconductors

We solve the Eliashberg equations for a two-dimensional, tight-binding band and anisotropic interaction due to exchange of phonons and antiferromagnetic spin fluctuations. For small band fillings, a mixture of simple and extendeds-wave pairing is stable, while for band fillings closer to half-filling thed-wave pairing state becomes stable. The density of statesN() becomes highly asymmetric in for smaller band fillings, which is an effect of particle-hole asymmetry. For thed-wave stateN() is linear in for small and exhibits a logarithmic singularity at the gap amplitude. For the mixeds-wave stateN() shows the BCS singularity at the gap edge. Antiferromagnetic spin fluctuations give rise to a pseudogap inN() for the normal state.     

Imaginary Squashing Mode Spectroscopy of Helium Three B

We have made precision measurements of the frequency of a collective mode of the superfluid ³He–B order parameter, the J=2⁻ imaginary squashing mode. Measurements were performed at multiple pressures using interference of transverse sound in an acoustic cavity. Transverse waves propagate in the vicinity of this order parameter mode owing to off-resonant coupling. At the crossing of the sound mode and the order parameter mode, the sound wave is strongly attenuated. We use both velocity and attenuation measurements to determine precise values of the mode frequency with a resolution between 0.1% and 0.25%.