L. Tewordt

Theory of thermal conductivity of the lattice for high-Tc superconductors

Abstract The observed peak below T c in the thermal conductivity К of YBa 2 Cu 3 O 7 can be explained fairly well by applying the BCS theory for lattice thermal conductivity limited by electron scattering. The contribution of longitudinal acoustic phonons to the electron-phonon coupling constant λ is estimated to lie within the weak coupling range. In addition to phonon-electron scattering we have taken into account scattering of phonons by structural defects like boundaries, point defects, and sheetlike faults. More detailed information about the strength of the phonon-electron scattering and the nature of the gap (weak or strong coupling) could be obtained from measurements of the anisotropy of К in single crystals.

THEORY OF THE DENSITY OF STATES OF PURE TYPE-II SUPERCONDUCTORS IN HIGH MAGNETIC FIELDS.

This paper deals with the theory of the density of states of pure type-II superconductors in high magnetic fields. An approximate expression of theGreens function is derived by using the fact that it has the periodicity of the lattice of flux lines in the center-of-mass coordinates. In comparison to the normal stateGreens function a correction term proportional to the absolute square of the order parameter arises. This is seen to act as a self-energy part depending strongly on the polar angleΘ of the “quasiparticle” momentum relative to the direction of the field. The corresponding density of states, as a function of the excitation energy, is found to vary from the gapless to the BCS type as the parameterΘ changes fromπ/2 to zero (orπ). The averaged state density varies gradually from a uniform to a BCS-like state density as the external field decreases sufficiently far below the upper critical field. The results of the present theory for the averaged density of states agree fairly well with the results due to a conjecture byMaki if the field is very close to the upper critical field.

Theory of phonon thermal conductivity for strong-coupling s-and d-wave pairing in high Tc superconductors

Abstract First we calculate the decay rate of a phonon due to phonon-electron interaction by employing strong-coupling theory for s- and d-wave pairing states. The resulting phonon thermal conductivity K exhibits a characteristic bump below Tc. The upturn of K below Tc is rounded off for the d-wave state in comparison to the BCS state. It becomes steeper for the s-wave state as the coupling strenght is increased. We calculate also the in-plane K ab and out-of-plane K c by taking into account the anisotropy of the phonon-electron interaction and momentum conservation below Tc is drastically reduced in comparison to that of K ab. It seems in the ab-plane. Then we find that the height of the bump of K c below Tc is drastically reduced in comparison to that of K ab. It seems that recent thermal conductivity data on single crystals of YBa2Cu3O7 and Bi-Sr-Ca-Cu-O can be fit somewhat better with the K ab for d-wave than for s-wave pairing.

Gap parameters and collective modes for 3He-B in the presence of a strong magnetic field

First we determine the 4 × 4 matrix Greens function for a p-wave pairing superfluid in a magnetic field where the order parameter is given by a real 3 × 3 matrix. For the B phase we take an order parameter which is equal to δ1 times a 3 × 3 matrix, yielding a rotation of angle θ about the z-axis and a dilatation δ2/δ1 along the z-axis. Then the self-consistency equation for the 4 × 4 matrix self-energy reduces to three equations for δ1, δ2, and cos θ, and a fourth equation for the renormalized Larmor frequency. We find that, for increasing field, δ1 increases and δ2 decreases with respect to the zero-field gap δ00. Above a (temperature-dependent) critical field we find δ2 = 0 and α2 = 90° corresponding to the planar state of lowest dipole energy. The correlation functions for the order parameter collective modes are calculated with the help of a previous theory. The results can be expressed in terms of six universal functions describing internal magnetization and virtual excitations of pairs of quasiparticles with all spin orientations. The complete set of eigenfrequencies as functions of the field is calculated for T = 0 and q = 0. The longitudinal NMR frequency is found to be almost independent of the field. We find a splitting of the pair-vibration frequencies (8/5) 1/2δ00 and (12/5)1/2δ00 which is linear in the field. This splitting is caused by fluctuations involving the spin-singlet component of the anomalous propagator. The splitting of the pair-vibration frequency (12/5)1/2δ00 (of the order 6H MHz, H in kG) should be observable by sound absorption experiments in strong magnetic fields.

Specific heat, thermal conductivity, and ultrasound attenuation in d-wave superconductors

Abstract Two d -wave pair states belonging to two-dimensional representations of the cubic and the hexagonal point groups, respectively, are investigated and compared to two p -wave states. It is shown that there is no characteristic difference between states with lines or points of nodes nor, in the absence of a magnetic field, between odd and even parity states. Serious discrepancies between theory and experimental results obtained for the heavy fermion systems UPt 3 and UBe 13 remain with respect to specific heat and thermal conductivity. Measurements of the anisotropy in the sound attenuation are suggested which could help to identify the most likely pair state.

Landé factors of collective mode multiplets in3He-B and coupling strengths to sound waves

In a previous paper we predicted a linear splitting of collective modes in3He-B with magnetic field, in particular, a fivefold splitting of the (8/5)1/2 Δ mode. A fivefold splitting of about the same size has been recently observed by Avenel, Varoquaux, and Ebisawa for the new sound attenuation peak. In this paper all 18 collective modes are classified in terms of total angular momentumJ=0, 1, 2, andJz by means of a unitary transformation to the nine eigenstates¦J, Jz〉. The Landé factors for the field splitting of the real and imaginary mode triplets and quintuplets [including the (12/5)1/2Δ mode quintuplet] are calculated for all temperatures. We also determine the sound dispersion relation. The angular dependence of the coupling constants of theJ=2 quintuplets is given by vY22Jz (θ)v, in agreement with the results of Avenel, Varoquaux, and Ebisawa for the new mode. We find a coupling constant of the (8/5)1/2 Δ mode to sound which is an order of magnitude smaller than that given by Koch and Wölfle. By comparing this with the experimental strengths we conclude that the particle-hole asymmetry parameter is about four times larger than that derived from the free-particle density of states.

Theory of thermal conductivity and nuclear relaxation rate for high temperature superconductors

Abstract We solve the strong-coupling equations for the self-energy of electrons in a two-dimensional tight-binding band, interacting via exchange of phonons, charge fluctuations, and spin fluctuations. The resulting dynamical spin and charge susceptibilities yield the nuclear spin-lattice relaxation rate 1/ T 1 and the phonon thermal conductivity κ p . For realistic values of the electron-phonon coupling λ ph and the on-site Coulomb interaction U / t we obtain a high T c , a rapid drop of 1/ T 1 below T c , and a broad peak in κ p below T c . The electronic thermal conductivity κ e is almost constant above T c , and it exhibits also a peak below T c due t o combined effects of inelastic and elastic electron scattering. Our results are in fair agreement with the actually measured quantities in Cu-O plane superconductors.

Self-consistent calculation of the longitudinal NMR for the Balian-Werthamer and Anderson-Brinkman-Morel states of superfluid3He

The general equations of motion for the Greens functions and correlation functions and the associated conservation laws for an anisotropic superfluid are derived. This leads to a simple commutator relation for the total angular momentum of the system and thep-wave pair amplitude. The longitudinal NMR frequencies for both the Balian-Werthamer (BW) and Anderson-Brinkman-Morel (ABM) states are calculated rigorously within the self-consistent random phase approximation scheme, taking account of all the degrees of freedom of the complex fluctuations of the order parameter (18 components) and their couplings via the dipole interactions. The results for the low-frequency resonances (ω≪Δ) are in agreement with those of Leggett except in the vicinity ofTc. In addition, in the presence of the dipole interaction, we find longitudinal resonances at ω=(8/5)1/2Δ and ω=21/2Δ for the BW and ABM states, respectively.

TEMPERATURE DEPENDENCE OF THE SURFACE UPPER CRITICAL FIELD OF SUPERCONDUCTING ALLOYS

The temperature dependence of the surface upper critical field,Hc3, nearTc is calculated for arbitrary values of the mean free pathl by taking into account the fourthorder term of the generalized Ginzburg-Landau theory. For finitel the boundary condition is modified such that the normal derivative of the energy gap at the surface becomes positive. The slope of the curveHc3/Hc2 versust=T/Tc att=1 is found to decrease monotoneously from zero to −1.040 as one goes from the “dirty” to the “clean” limit.

COLLECTIVE MODES IN HIGH-TEMPERATURE SUPERCONDUCTORS

The role of collective modes in various experiments on the cuprates is investigated. We calculate the neutron scattering, photoemission [angle-resolved photoemission spectroscopy (ARPES)], and Raman-scattering intensities below T(c) within the fluctuation-exchange approximation for the two-dimensional Hubbard model. It is shown that the large peak in the dynamical spin susceptibility arises from a weakly damped spin-density-wave collective mode. This gives rise to a dip between the sharp low-energy peak and the higher binding energy hump in the ARPES spectrum. Furthermore, we show that the collective mode of the amplitude fluctuation of the d-wave gap yields a broad peak above the pair-breaking threshold in the B(1g) Raman spectrum. [S0163-1829(98)00142-8].