P. Wölfle

The Superfluid Phases of Helium 3

A comprehensive treatment of the theory of superfluid helium-3 is presented in this book. This treatment also illustrates many of the principal themes of theoretical condensed matter physics over the past two decades. The generalized BCS (Barden-Cooper-Schrieffer) pairing theory and the experimental properties of superfluid helium-3 are treated in detail. Extensive treatment of broken symmetries and their relation to macroscopic order and of the closely related topics of superflow and texture, defects in the order parameter field, and the dynamics of the nuclear spins as probed by nuclear magnetic resonance is included. This book should serve as a valuable reference for anyone working on superfluid helium-3 or on the closely related topics of unconventional superconductivity in heavy-electron metals and superfluidity of neutron star interiors.

Fermi-liquid instabilities at magnetic quantum phase transitions

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

Resonant impurity scattering in heavy fermion superconductors

Abstract The effect of resonant impurity scattering on the properties of superconducting heavy fermion compounds proposed recently by Pethick and Pines is investigated within a self-consistent theory of pair-breaking. We discuss the thermodynamic and transport properties of axial and polar type order parameters for a range of impurity concentrations and scattering phase shifts. The results for the polar state with impurity concentrations ni≅10−4 and phase shifts Δo close to the unitarity limit π 2 appear to give a good description of data on UPt3. Unusual behavior is predicted to occur in a gapless regime below a temperature T o ≅T c ·(n i T F /T c ) 1 2 .

Boundary effects in fluid flow. Application to quantum liquids

The effect of boundaries on the flow of rarefied gases is considered. For an excitation gas of arbitrary statistics and energy-momentum relationship we determine the magnitude of the slip length and the flow between parallel plates mostly by variational methods. Our approximate method avoids the need to solve integral equations numerically and yields in the stationary case better than 1% agreement with known exact results for the classical Maxwell-Boltzmann gas. Our general results are primarily applied to normal and superfluid Fermi liquids. We calculate the surface impedance of an oscillating plate and determine the frequency-dependent slip length for frequencies ranging from the hydrodynamic to the collisionless limit. Our results are applied to the analysis of viscosity measurements based on a torsional oscillator or a vibrating wire. The slip effects are shown to be very important for realistic experimental parameters, especially at low temperatures in the superfluid B phase of liquid 3He.

Thermally assisted hopping transport in disordered systems

The response to an external field of localized electrons coupled to phonons is investigated. The low frequency (ω<T) linear response function is shown to obey a kinetic equation. The transition probabilities (including multiphonon contributions) can be expressed in terms of the dynamical correlation functions(k, ɛ) of the phonons. The low temperature d.c. conductivity in three dimensions obeys a law σ(0)=σ0 · exp(− (T0/T)1/4). By a combined variational and “nearest neighbor” approximation upper limits for the exponential as well as the pre-exponential factor are obtained. In two dimensions the 1/4 in the exponent has to be replaced by 1/3. The one-dimensional case requires separate considerations which do not simply lead to an exponent 1/2.An expression for the thermopower in the hopping regime is derived and evaluated.

Theory of thermally assisted electron hopping in amorphous solids

Using a kinetic equation for thermally assisted hopping processes a general expression for the conductivity σ(ω) in disordered systems in terms of the collision operator is derived. The d.c. conductivity is determined by the low lying eigenstates of the collision operator. The eigenvalue equation bears a close analogy to the corresponding problem of atomic vibrations in disordered systems. The calculation of the d.c. conductivity is analogous to the calculation of elastic constants from the dynamical matrix. Using a variational approach for the low lying eigenstates we have found a law In σ(0)=const-(To/T)1/4. The error in the value ofTo introduced by our trial function has been calculated and found to be reasonably small.

Nonequilibrium transport through a Kondo dot in a magnetic field: perturbation theory and poor man's scaling.

We consider electron transport through a quantum dot described by the Kondo model in the regime of large transport voltage V in the presence of a magnetic field B with max(V, B) >> T K . The electric current I and the local magnetization M are found to be universal functions of V/T K and B/T K , where T K is the equilibrium Kondo temperature. We present a generalization of the perturbative renormalization group to frequency dependent coupling functions, as necessitated by the structure of bare perturbation theory. We calculate I and M within a poor mans scaling approach and find excellent agreement with experiment.

Kondo effect in quantum dots at high voltage: universality and scaling.

We examine the properties of a dc-biased quantum dot in the Coulomb blockade regime. For voltages V that are large compared to the Kondo temperature T(K), the physics is governed by the scales V and gamma, where gamma approximately V/ln(2)(V/T(K)) is the nonequilibrium decoherence rate induced by the voltage-driven current. Based on scaling arguments, self-consistent perturbation theory, and perturbative renormalization group, we argue that due to the large gamma the system can be described by renormalized perturbation theory in 1/ln(V/T(K))<<1. However, in certain variants of the Kondo problem, two-channel Kondo physics is induced by a large voltage V.

Dynamical impurity spin susceptibility in metals

The longitudinal and transverse impurity spin susceptibilities are expressed exactly in terms of holomorphic self-energies. Within thes-d model these self-energies are calculated in lowest order perturbation theory thus yielding reasonable approximations for the susceptibilities valid for all temperatures and magnetic fields above the Kondo regime and in the whole frequency domain including the hydrodynamical one. The transverse susceptibility and the longitudinal nuclear spin susceptibility are found to be satisfactorily described by Blochs equations. In the low-temperature regime the longitudinal relaxation timeT1 exhibits a nontrivial spin and temperature dependence. At low temperatures and high fields the longitudinal localized electron spin susceptibility is found to show a non-Lorentzian double-peak line shape which cannot be described by Blochs equations.

Transport and relaxation properties of superfluid 3He. I. Kinetic equation and Bogoliubov quasiparticle relaxation rate

The kinetic equation for Bogoliubov quasiparticles for both the A and B phases of superfluid 3He is derived from the general matrix kinetic equation. A condensed expression for the exact spin-symmetric collision integral is given. The quasiparticle relaxation rate is calculated for the BW state using the s-p approximation for the quasiparticle scattering amplitude. By using the results for the quasiparticle relaxation rate, the mean free path of Bogoliubov quasiparticles is calculated for all temperatures.