Sum rules and the landau theory of fermi liquids

The Landau theory predicts spectral weight functions for density and spin-density fluctuations which in the long-wavelength, low-frequency limit should be equal to the true spectral weight functions of a system of interacting fermions. This correspondence plus well-known frequency sum rules provides a means to examine the Landau quasiparticle interaction parameters. Two inequalities are derived:F ₁ G ₁ and another relating the first three spin-symmetric Landau coefficients to the radial distribution function and the two-particle potential. We find that the third-moment sum rule is not entirely exhausted by Landau-accountable excitations, and therefore it is the highest order sum rule which can still probe the theory. A third-moment sum rule for the spin-spin correlation function is derived and is found to have an unexpected dependence onk, i.e., one that disagrees with the corresponding Landau prediction. We do not examine this result in detail, but merely conjecture that it may indicate a basic weakness in the Landau theory of spin-density fluctuations.     

Shadow Bands, Gap and Pseudogaps in High-Tc Superconductors

Within the framework of the Charge Density Wave Quantum Critical Point(CDW-QCP) scenario for high-T _c superconductors (HTCS) we introduce a modelfor tight-binding electrons coupled to quasi-critical fluctuations. In thenormal state our model reproduces features the Fermi Surface (FS) observedin ARPES measurements on optimality doped Bi2212, such as the anisotropicsuppression of spectral weight around the M points of the Brillouinzone. The spectral density is characterized by a transfer of spectral weightfrom the main quasiparticle peak to dispersing shadow peaks which originatebranches of a shadow FS. In the superconducting state our model reproducesthe d-wave symmetry of the gap parameter, which results from a balancebetween small-q attraction and large-q repulsion. The gap parameter isenhanced due to cooperative effects of charge and spin fluctuations.     

Andreev Reflection in Unitary and Non-Unitary Triplet States

The quasiparticle reflection and transmission properties at normal conductor-superconductor interfaces are examined for unitary and non-unitary spin triplet pairing states recently discussed in connection with Sr ₂ RuO ₄ . We find resonance peaks in the Andreev reflection amplitude, which are related to surface bound states in the superconductor. They lead to conductance peak features below the quasiparticle gap in the superconductor. The symmetry of the pairing state determines the specific dependence of the peak on the angle of incidence. Based on this observation we propose a possible experiment which allows to distinguish between different superconducting states.     

Nuclear relaxation and impurity magnetism in superconducting La1−c Gd c Al2 and La1−c Ce c Al2

The¹³⁹La spin-lattice relaxation rate in the normal and superconducting states of La_1–c Gd _c Al₂ and La_1–c Ce _c Al₂ alloys has been studied as a probe of the effect of magnetic impurites on superconducting quasiparticle excitations in these systems. Comparison of the experimental data with the theory of pair breaking by magnetic impurities verifies the predicted broadening of the peak in the spectrum of quasiparticle excitations. The dependence of the relaxation rate on the strength of the coupling between conduction electrons and impurities is not fully resolved in the present experiments.Work supported in part by the U.S. National Science Foundation.Laboratoire associé au CNRS.     

Shadow Bands, Gap and Pseudogaps in High-Tc Superconductors

Within the framework of the Charge Density Wave Quantum Critical Point(CDW-QCP) scenario for high-T _c superconductors (HTCS) we introduce a modelfor tight-binding electrons coupled to quasi-critical fluctuations. In thenormal state our model reproduces features the Fermi Surface (FS) observedin ARPES measurements on optimality doped Bi2212, such as the anisotropicsuppression of spectral weight around the M points of the Brillouinzone. The spectral density is characterized by a transfer of spectral weightfrom the main quasiparticle peak to dispersing shadow peaks which originatebranches of a shadow FS. In the superconducting state our model reproducesthe d-wave symmetry of the gap parameter, which results from a balancebetween small-q attraction and large-q repulsion. The gap parameter isenhanced due to cooperative effects of charge and spin fluctuations.     

Theory of the AC Josephson effect in triplet superconducting junction

The quasiparticle and AC Josephson current in superconductor / insulator / superconductor (S/I/S) junctions including a triplet p-wave superconductor are calculated for arbitrary transmission of the junction. As a triplet pairing state we select one of the unitary pairing states which is a promising candidate for the superconducting state in Sr ₂ RuO ₄ . In p-wave superconductor / insulator /p-wave superconductor junction, both quasiparticle current and AC Josephson current are enhanced near zero-bias voltage due to the existence of zero energy state of p-wave superconductors. For the s-wave superconductor/ insulator / p-wave superconductor junction, the quasiparticle current at low voltage is suppressed due to the energy gap of s-wave superconductor. The first Fourier component of the AC Josephson current vanishes due to the difference of the parity between the two superconductors.     

The flux-flow hall effect in type II superconductors. An explanation of the sign reversal

We consider a time-dependent Ginzburg-Landau (TDGL) model modified to take into account two mechanisms responsible for the Hall voltage in superconductors: the usual effect of the magnetic field on the normal current, and the vortex traction by the superflow. For the BCS model of superconductivity, the contribution of the vortex traction is proportional to the energy derivative of the quasiparticle density of states. Our theory gives the correct order of magnitude for the Hall angle in the mixed state. It predicts that the vortex-traction mechanism results in a negative Hall angle for the quasiparticle spectrum with a positive energy derivative of the density of states averaged over the Fermi surface, and vice versa. For the Fermi surface with a complicated shape, the sign of the Hall effect in the mixed state can be different from that in the normal state. If the signs are opposite, the Hall angle changes its sign as a function of the magnetic field belowH _c2 .     

Mobility tensor of negative ions in superfluid 3He-A

The mobility tensor of negative ions in the A phase of superfluid ³He is calculated for temperatures close to T _c . In this regime the scattering of superfluid quasiparticles from an electron bubble is practically elastic and the mobility tensor is expressed in terms of momentum transfer cross sections for an ion at rest. These generalized transport cross sections are obtained from the quasiparticle-ion scattering T-matrix, which we evaluate in terms of the normal state scattering amplitude. The p-wave pairing correlations in the intermediate states result in important interference effects among all partial waves in the scattering process, and, in addition, for the low-energy quasiparticles they lead to resonant states below the gap edge. These phenomena modify the scattering amplitude in the superfluid in an essential way and the differential quasiparticle-ion cross section is found to display strongly anisotropic, energy-dependent variations on the scale of the superfluid energy gap. We find that, in contrast to simple approximations, for low quasiparticle energies the parallel and perpendicular momentum transfer cross sections are very different from one another. Close to T _c , the calculated mobility remains rather isotropic, but at lower temperatures the anisotropy is considerably larger than predicted by simple approximations for the cross section. The computed results are compared with the available measurements.Supported in part by U.S. National Science Foundation Grants DMR78-21068 and DMR78-21069.     

Cluster Size and Shape Effect on the Electronic Structure of the Hubbard Model Within the Norm-Conserving Cluster Perturbation Theory

Within a new norm-conserving approach to the cluster perturbation theory (CPT) for the 2d Hubbard model we study the effect of the cluster size and shape on the electronic structure. We have compared two type of clusters, 4-cluster (2×2) and 5-cluster (cruciform of 5 atoms). With 4-cluster we can treat exactly the first and second neighbours correlations, C ₁ and C ₂. With 5-cluster the third neighbour correlations C ₃ are also treated exactly. The band structure in the CPT with 4- and 5-clusters differs remarkably. The quasiparticle spectral weight map for 5-clusters is very similar to the Quantum Monte Carlo (QMC) and the variational CPT data. With increasing doping, small hole Fermi surface transforms into conventional Fermi-liquid type large Fermi surface through Lifshitz quantum phase transitions.     

A Critical Examination of the Spin Dynamics in High-Tc Cuprates

A critical examination of the spin dynamics in high-T _c cuprates is made in the light of recent inelastic neutron scattering results obtained by different groups. The neutron data show that incommensurate magnetic peaks in YBCO belong to the same excitation as the resonance peak observed at (/a, /a). Being observed only in the superconducting state, the incommensurability is rather difficult to reconcile with a stripe picture. We also discuss the link between the resonance peak spectral weight and the superconducting condensation energy.     

Electronic Spectra of Iron Pnictide Superconductors: Influence of Multi-orbitals Hopping and Hund’s Coupling

We present a theoretical study of the electronic spectral function of iron-pnictide superconductors like LaFeAs(O, F) material. We have attempted two-band tight-binding model Hamiltonian containing various orbitals hopping energies, intra- and inter-band electronic correlations and Hund’s coupling energy in Fe 3d orbitals. The expression of a single particle spectral function within BCS-mean-field Green’s function approach for superconducting state of iron pnictides is obtained. The spectral function at different points of the Brillouin zone is numerically calculated for extended s-wave pairing symmetry as a function of various model parameters applicable for these systems. It is pointed out through numerical analysis that on increasing nearest-neighbor hopping (t ₁) between (d _xz /d _yz ) σ-orbitals, the spectral function A(k,ω) shifts towards the Fermi level and provides favorable conditions for band splitting effects in the form of two well separated peaks in the electronic spectral as observed in iron pnictides angle-resolved photoemission spectroscopic (ARPES) measurements. On increasing t ₂ (nearest-neighbor hopping between d _xz /d _yz π-orbitals), the spectral function shows prominent peak with increase in spectral weight close to the Fermi level at the (π,0) and (0,0) points of the Brillouin zone, while the quasi-particle peak shifts away from the Fermi level at the (π,π) point with decreased spectral weight. The bonding peak of spectral function get suppressed while the antibonding spectral peak becomes prominent with increasing t ₃ (next nearest-neighbor hopping between same orbitals of d _xz /d _yz ) at (π,π) of the Brillouin zone. Further, intra-band Coulomb correlations shift the spectral peak downward with respect to Fermi level along with suppression of the spectral weight. The Hund’s coupling term try to pile up spectral weight close to Fermi level and support to stabilize superconducting state in these systems. The variation of the spectral function within the two-band model is in qualitative accordance with existing ARPES measurements and theoretical investigations in iron-pnictide superconductors.     

Temperature dependence of the sound velocity in liquid4He

We have measured the temperature dependence of the sound velocity in liquid ⁴ He from 0.07 to 0.7 K for frequencies from 12 to 105 MHz. While the data show an approximateT ⁴ temperature dependence, the frequency ordering of the curves is observed to undergo an inversion at about 0.2 K. Above this temperature we confirm that the velocity shift decreases with frequency, while below this temperature we now find that the velocity shift increases with frequency as predicted by theory.Based on work performed under the auspices of the U.S. Atomic Energy Commission.     

Tunneling potentials associated with thermoelectric quasiparticle transport in superconductors

A superconductor in a thermal gradient assumes a steady state with counterflowing super and normal currents. A quasiparticle transport theory is presented for this current, and the resulting nonequilibrium quasiparticle distribution function is used to discuss NIS tunneling. For zero tunneling current, we derive a bias voltage which is quadratic in T and which is of roughly the same magnitude as the linear effect recently measured by Falco.Work performed under the auspices of the U.S. Department of Energy.     

The velocities of first and second sound in dilute solutions of3He in superfluid4He at very low temperatures

A unified theory of first and second sound in dilute solutions of ³ He in superfluid ⁴ He at very low temperatures is presented. The theory is based on the detailed semimicroscopic model for the ³ He quasiparticle excitations described by Disatnik and Brucker a few years ago. In contrast with Khalatnikov's macroscopic theory, the application of this model enables the derivation of relatively simple expressions for the sound velocities in which no omissions of terms representing contributions due to the thermal expansion are made. The sound velocities are given in the final expressions in terms of various parameters of the ³ He quasiparticle spectrum and effective interaction. These expressions are both highly accurate and easy to use over a wide temperature regime spanning from the quantum limit to temperatures of the order of the ³ He quasiparticle degeneracy temperature. The actual application of the theory to measurements of the sound velocities is described in detail. Numerical values or estimates for various characteristic parameters of the ³ He quasiparticle system, including in particular the ³ He quasiparticle effective mass, are obtained from the comparison between the theory and the experiment. The example of the second sound velocity is used to illustrate a procedure for analyzing data from very low-temperature measurements of the equilibrium properties of the solutions, which is expected to produce meaningful information regarding the parameters of the basic model. In practice, the theory is found to be in a very good accord with the measurements of the sound velocities. The result obtained for the zero concentration limit of the ³ He quasiparticle effective mass (m ₀ =2.19m ₃ ) is somewhat lower than the empirical estimates reported in the past. On the other hand, this result is in very good agreement with variational calculations based on the detailed microscopic theory of the solutions. A discussion of this and other results obtained from the comparison between theory and experiment is included.Work supported in part by the United States-Israel Binational Science Foundation.Killed in action, 16 October 1973.     

Spin- and charge-fluctuation effects on dynamic conductivity in Cu-O plane superconductors

A self-consistent microscopic theory for the 2D Hubbard Hamiltonian and additional electron-phonon interaction yields below T _c a gap in the quasiparticle decay rate as well as in the spin and charge fluctuation spectra. The mass enhancement and the quasiparticle decay rate exhibit in the normal state marginal Fermi liquid behavior while in the superconducting state the quasiparticle character is restored. These properties lead to anomalous behavior of the dynamic conductivity: considered as a function of temperature a peak evolves at T c as the frequency is decreased well below 2. In the optical conductivity, considered as a function of frequency, a gap between 2 and 4 opens rapidly as T is decreased below T c. Our results are in qualitative agreement with experiments on high-T c superconductors.     

Attenuation of zero sound in oriented liquid3He-A

Systematic measurements of the change – _c of the absorption coefficient for zero sound in³He-A from its value atT _c are presented for both 24.08 and 33.53 bar and several frequencies. The³He-A is oriented by means of a magnetic field, so only the case where field and sound directions are parallel give results which can be reliably compared with theory. We find that for 5-MHz zero sound at temperatures well below the collective modes peak there is a substantial anisotropy of the attenuation. We also find at high enough frequency a linear relationship between the sonic frequency and the location on a(1–T/T _c)^1/2 scale of the collective modes peak forl·q=0. Comparison of theory and experiment for these data is excellent and suggests that the method may be an accurate one for measuring the temperature dependence of the energy gap in³He-A.Work supported by the U.S. Energy Research and Development Administration under contract number E(04-3)-34 P.A. 143.     

Thermoelectric generation of charge imbalance at a superconductor-normal metal interface

The thermoelectric voltage produced across a superconductor-normal metal-superconductor (SNS) sandwich by an applied heat current has been measured in Pb-Cu-PbBi and In-Al-Sn as a function of temperature. The observed divergence of the thermoelectric voltage near T _c is attributed to a charge imbalance region decaying into the superconductor from the NS interface over the quasiparticle diffusion length _Q ^*. The charge imbalance is generated by thermoelectrically driven quasiparticle currents in the super-conductor. It contributes a voltage per unit heat power given by V_s/P = _Q*S/A, where A is the sample cross-sectional area, and S and are the thermopower and the thermal conductivity of quasiparticles in the super-conductor. For Pb and In, we find the measured thermopower in the super-conducting state to be slowly varying with temperature near T _c and consistent in magnitude with normal state values. This result is in agreement with theoretical predictions of thermoelectric effects in superconductors but contrary to previous experimental results obtained by other methods.Supported in part by the Division of Materials Science, Office of Basic Energy Sciences, U.S. Department of Energy under contract No. W-7405-Eng. 48.     

Anisotropy in Quasiparticle Density of States in the Vortex State of an Orthorhombic d-Wave Superconductor

The quasiparticle density of states is calculated in the vortex state of an orthorhombic d-wave superconductor as a function of the orientation of the external magnetic field (H ) in the CuO ₂ -plane. Because of the existence of chains oriented along the y-axis in YBCO, its in-plane properties are highly anisotropic and in the superconducting state a predominantly order parameter will also contain a subdominant s-wave admixture allowed by the orthorhombic crystal space group. In a simple anisotropic effective mass model for the band structure and a d + s gap we compute the quasiparticle density of states as a function of the orientation () of H with respect to the a-axis in the CuO ₂ plane. As a function of we find a two fold pattern of behavior with minima at the angles where the Fermi velocity at the nodal momentum is in the direction of the external field. For an untwinned single crystal the resulting anisotropy of the specific heat at low temperatures should be measurable. It is greatly reduced in twinned samples     

Nuclear spin relaxation and quasiparticle excitations in superconducting aluminum-3d alloys

Aluminum-27 nuclear spin-lattice relaxation times T ₁ have been measured in the normal and superconducting states of dilute alloys of Mn, Cr, and V in aluminum. These measurements prove the spectrum of thermally excited quasiparticle states in the superconductor and its modification by nonmagnetic resonant impurities. Theoretical studies of such systems indicate that in the Hartree-Fock (HF) approximation the BCS character of the host is basically retained in the alloy, with a reduced pairing interaction and a small additional broadening of quasiparticle states at the gap edge. Spin-fluctuation improvements on the HF approximation renormalize the parameters involved, but do not change the basic picture. Our T ₁ data indicate gap edge broadening an order of magnitude greater than predicted. The discrepancy is nearly as large for V and Cr impurities as for Mn, which makes it unlikely that localized spin fluctuations play an important role in the broadening. Recent speculation on the effect of dislocation pinning by resonant impurities may be relevant to these results.Work supported by the U.S. National Science Foundation under Grants DMR73-02395-A01 and DMR-09403.