The path integral model ofD-pairing for HTSC,heavy fermion superconductors,and superfluids

A model ofd-pairing for superconducting and superfluid Fermi-systems has been formulated within the path integration technique. By path integration over fast and slow Fermi-fields, the action functional (which determines all properties of model system) has been obtained. This functional could be used for the determination of different superconducting (superfluid) states, for calculation of the transition temperatures for these states, and for the calculation of the collective mode spectrum for HTSC, as well as for heavy fermion superconductors.     

Effect of resonant impurity scattering on collective mode peaks in the ultrasound attenuation of heavy fermion superconductors

We have calculated the attenuation of longitudinal ultrasound due to real order parameter fluctuations in impure polar and planarp-wave superconductors. The quasiparticle self-energy and the corresponding vertex corrections have been included in thet-matrix approximation for arbitrary scattering rate =1/2_N and all scattering phase shifts _N (0 _N/2). We obtain sound attenuation peaks belowT _c whose heights, positions, and shapes depend on ₀ (sound frequency), (₀), _N, and (coupling strength due to particle-hole asymmetry). The peaks become much more distinct and sharper for _N =/2 (resonant scattering by impurities) than for _N=0 (Born approximation). By choosing , _N, and suitably, qualitative agreement between calculated and observed peaks in UBe₁₃ and UPt₃ can be achieved.     

Quantum tunneling of vortices in cuprate and heavy fermion superconductors

In high-T_c and in heavy fermion superconductors at low enough temperatures, pinned vortices move from one potential well to another mainly by quantum tunneling. In the superconducting cuprates, the measured creep rates at low magnetic induction and in the T 0 limit are in excellent agreement with the values calculated within the framework of the Quantum Collective Creep theory. In the heavy fermion superconductor UPt₃, the measured rates at T 0 are much higher than the theoretical values, giving evidence that the low temperature motion of vortices in this material is possibly related to its unconventional character.We thank the Swiss National Foundation for financial support.     

Ultrasound attenuation peaks due to order parameter collective modes in impure superconductors with strong electron-hole asymmetry

First we develop the general theory of order parameter collective modes and their sound attenuation in dirty superconductors with even-parity pairing. For the BCS state the theory yields a peak in the attenuation of longitudinal ultrasound whose height is proportional to _o[J(s)]² and whose positiont _p 1 -T _p /T _c and width are proportional to _o/ = 2sql(s=v _s /v _F ). Here, is the particle-hole asymmetry parameter,J(s) a given function, _o the sound frequency, and =1/2 _N ^–1 the normal state scattering rate. For T _c /T _o 0.1,s=2/3, and _o/ ql « 1, the peak agrees qualitatively with the peaks found earlier for the polar and axial states. However, at low temperatures the attenuation goes like T⁴ instead ofT ³. We conclude that the observed longitudinal ultrasound peaks in the heavy-fermion superconductors UBe₁₃ and UPt₃ can be explained equally well by any anisotropic state having nodes in the gap, in particular, by a conventional state whose gap has the full symmetry of the Fermi surface. The nature of the state is reflected mainly in the dependence of the peak on the direction of sound propagation.     

Analysis of intermediate boson spectra from FIR data for HTSC and heavy fermion systems

Calculations of the effect of intermediate bosons on the optical properties of the normal state are used to analyze the spectra of these bosons. For high temperature superconductors these spectra are in agreement with the standard electron-phonon model (the end of the spectrum is near 800 cm^–1) with a moderate coupling constant =1–1.5. For the heavy fermion compound UPt₃ the spectrum of intermediate bosons is consistent with neutron data for spin fluctuations.This work was partially supported by ISF and RFFI (No 94-02-04186a) grants.     

Microwave measurements on the heavy fermion superconductors UPt3 and UBe13

The complex microwave impedance at 11.5 GHz was measured in the superconducting state of two well characterized heavy fermion single crystals, UPt ₃ and UBe ₁₃ . This microwave photon energy is about 30% and 20% of the zero-temperature energy gap, respectively, and is higher than previous measurements. The results for UBe ₁₃ seem to be well described by the Mattis-Bardeen theory in the dirty-limit for a conventional superconductor. However, the behavior in UPt ₃ deviates from this conventional theory even when paramagnetic impurity scattering effects are taken into account.     

The influence of high-frequency fields on the order parameter in pure,type I superconductors

The behavior of the order parameter in pure, type I superconductors in the presence of high-frequency fields is discussed. It is shown that in second order in the field the order parameter is disturbed at considerably larger distances from the surface than the penetration depth and the coherence length.     

The collective excitations in3He-A1

The collective mode spectrum of the superfluid A₁-phase of³He is calculated by a path integration technique. It is shown that there is one pairbreaking mode E(k=0)₀ (1, 96-i0, 31) and two clapping modes E(k=0)₀(1, 17-i0, 13), eight modes E=2µH and one goldstone mode E=0. Six other modes have an imaginary spectrum. This fact is connected with the instability of the A₁-phase under small perturbations.     

The model ofd-pairing in CuO2 planes of HTSC and the collective modes

We develop here for the first time a 2D path integral model of d-pairing in HTSC, which is analogous to the 3D model created earlier by Brusov and Brusova. Within this model we calculate the entire collective mode spectrum for all superconductive states of CuO₂ planes arisen from their symmetry classification. There are four collective modes in each phase. We found two high frequency modes in each phase while two remains modes seem to be Goldstone or quasi-Goldstone ones (having vanishing energy at zero momentum). It turns out that the collective mode spectrum in the phases and is the same.     

Coupling of order parameter collective modes to spin density in3He-B

We derive a general expression for the dynamic spin susceptibility of³He-B which is valid for all magnetic fields. The coupling of real and imaginary modes by particle-hole asymmetry is taken into account. Then we calculate the contribution of the mode at frequency =2 – 1/4 ( is the effective Larmor frequency) to the transverse susceptibility. The spectral weight of this mode in magnetic resonance absorption is proportional to (/)^1/2 (–)², where and are particle-hole asymmetry parameters. From the experimental coupling strength of the real squashing mode to sound we estimate (–)²10^–4. The dynamic susceptibility satisfies the sum rules of Leggett. Finally we point out the difficulties in calculating the transverse NMR frequency of³He-B. These difficulties arise from theS _z =0 Cooper pairs and from the coupling ofJ _z =±1 modes forJ=1 andJ=2.     

Dynamical fluctuation of the order parameter and diamagnetism of superconductors. I. Dirty limit

Limiting ourselves to dirty superconductors, we study theoretically the fluctuation-induced diamagnetism above the superconducting transition. We find that the dynamical fluctuation is extremely important except in the immediate vicinity of the transition region [i.e.,TT _c(H) orHH _c2(T), whereH _c2 is the upper critical field] and that this contribution does account for a large discrepancy between previous calculations and the recent experiment by Gollub, Beasley, and Tinkham.     

The collective excitations of superfluid4He in aerogel glass

When liquid⁴He is condensed in porous aerogel glass (typical pore size ≈ 500 Å), many of the superfluid properties are significantly altered. Neutron inelastic scattering has been used to measure the collective phonon-roton excitations of liquid⁴He in this restricted geometry. Although at low temperature (1.3 K) the observed dispersion relation is identical to that of bulk⁴He, its temperature dependence is shown to be different. Previously unexplained superfluid fraction data are shown to be derivable from these microscopic measurements. An intrinsic broadening of the excitations associated with the restricted geometry is also present. Possible microscopic explanations for the unusual temperature variation of the collective excitation energies are discussed.     

Magnetism and superconductivity in heavy fermion systems

We discuss some consequences of the interplay between magnetism and superconductivity in the two heavy fermion systems URu₂Si₂ and UPt₃, notably on the temperature dependence of the specific heat, on possible observation of Larkin-OvchinnikovFulde-Ferrel phase, and on the anisotropy of the upper critical field. We demonstrate that in UPt₃, a clear double steep superconducting transition can be obtained reversibly.     

Ultrasonic studies of the heavy fermion compounds

A review of ultrasonic measurements on the three heavy fermion compounds UPt ₃ , URu ₂ Si ₂ and CeCu ₆ is given. These compounds show one or more of the three types of co-operative behavior; Kondo-like effect, antiferromagnetism and superconductivity; all these features are observed as ultrasonic anomalies. Both UPt ₃ and CeCu ₆ show a strong coherence effect which is akin to a Kondo-like transition in the electronic system. Velocity anomalies are found at the antiferromagnetic transition for URu ₂ Si ₂ . UPt ₃ also has an antiferromagnetic transition which is believed to influence the subsequent superconducting ordering. For UPt ₃ , the superconductivity is of an unconventional nature; multiple superconducting phases have been observed and a complete phase diagram has been obtained from high resolution velocity measurements.     

Electronic and vibrational excitations in layered highT c superconductors

In the series of the layered highT _c superconductors (A)_1,2 B₂Ca _n−1Cu _n O_2n+3,4 (A=Tl or Bi;B=Ba or Sr), withn=number of consecutive Cu-O layers, the electron energy states of some of the Tl-based systems have been investigated. The electron and phonon dispersion curves have been obtained. The electronic states near the Fermi level are dominated by the hybridized Cu(d) and the O(p) orbitals. The dispersion curves are highly two-dimensional with very small dispersion alongc-axis. The number of bands is enhanced with increase in the number of the consecutive Cu-O planes (n). The present results agree with those obtained earlier for other superconducting phases. The phonons are overall dominated by the vibrations of the light mass oxygen atom modes both lying in or outside the Cu-O planes. The low-frequency phonons involve the motions of the heavier Tl, Ba atoms etc.     

Electronic structure and the structure of the order parameter in high-T c superconductors based on copper oxides and iron pnictides

Experimental data on the symmetry of the superconducting state in the high-T _c superconductors based on copper oxides and iron pnictides have been analyzed using a space group approach to the wavefunction of a Cooper pair. We have found the irreducible representations of the crystal symmetry groups of these materials for singlet states with zero total momentum corresponding to experimental data on the structure of their order parameter.     

Spiral magnetism and collective excitations in doped Hubbard models

We discuss the ground state properties and the collective dynamics of spiral magnetic states in the two dimensional Hubbard model. In particular we present the phase diagram in the presence of a finite next-nearest-neighbor hopping integral t. In contrast to the plain t Hubbard-model we find a region of stable antiferromagnetism in an extended interval of electron (hole) doping off half filling for a negative (positive) ratio of t/t. In addition we investigate the coupled charge and spiral spin-excitations off half filling. The resulting collective modes are found to be highly anisotropic and strongly Landau damped.     

Magnetic collective excitations in the B phase of superfluid He-3

The dynamical susceptibility of the B phase of superfluid He-3 in the presence of dipolar coupling is calculated in the collisionless regime. Two poles of the susceptibility that correspond to the spin wave and the mode with energy gap (2/5)^1/2 2 are found. The result agrees with that of Tewordt and Einzel qualitatively and contradicts the recent work by Maki. The residue of the high-frequency mode becomes remarkable near the transition temperature. The dispersion relations of these modes atT=0 K and near the transition temperature are given in the most general form.     

The structure of fermion density matrices. III. Long-range order

Generalizing C. N. Yang's discussion of the onset of superconductivity, a criterion is proposed for the existence of infinite or localized long-range order. Questions are raised concerning the spectrum of the reduced Hamiltonian and the statistics of Fermi pairons.     

Reactive effects of core fermion excitations on the inertial mass of a vortex

The time-dependent Schrödinger equation for a fermion two-dimensional super-fluid containing a moving vortex is solved using the adiabatic approximation. The expectation value of the linear momentum of the vortex is found dominated by core fermion excitations. The resulting inertial vortex mass, obtained in the adiabatic limit, is larger than the standard core mass by a factor of (k_F,)₂ where , is the coherence length at T = 0. Anamalous velocity dependence of the mass, associated with the breakdown of the adiabatic approximation, is predicted.