Transport properties of clean and disordered superconductors in matrix field theory

A comprehensive field theory is developed for superconductors with quenched disorder. We first show that the matrix field theory, used previously to describe a disordered Fermi liquid and a disordered itinerant ferromagnet, also has a saddle-point solution that describes a disordered superconductor. A general gap equation is obtained. We then expand about the saddle point to Gaussian order to explicitly obtain the physical correlation functions. The ultrasonic attenuation, number density susceptibility, spin density susceptibility and the electrical conductivity are used as examples. Results in the clean limit and in the disordered case are discussed respectively. This formalism is expected to be a powerful tool to study the quantum phase transitions between the normal metal state and the superconductor state.Comment: 9 page

Fluctuation-Driven Quantum Phase Transitions in Clean Itinerant Ferromagnets

The quantum phase transition in clean itinerant ferromagnets is analyzed. It is shown that soft particle-hole modes invalidate Hertz's mean-field theory for $d \leq 3$. A renormalized mean-field theory predicts a fluctuation-induced first order transition for $1 < d \leq 3$, whose stability is analyzed by renormalization group techniques. Depending on microscopic parameter values, the first order transition can be stable, or be pre-empted by a fluctuation-induced second order transition. The critical behavior at the latter is determined. The results are in agreement with recent experiments.Comment: 4 pp., REVTeX, no figs; final version as publishe

Nonanalytic Magnetization Dependence of the Magnon Effective Mass in Itinerant Quantum Ferromagnets

The spin wave dispersion relation in both clean and disordered itinerant quantum ferromagnets is calculated. It is found that effects akin to weak-localization physics cause the frequency of the spin-waves to be a nonanalytic function of the magnetization m. For low frequencies \Omega, small wavevectors k, and small m, the dispersion relation is found to be of the form \Omega ~ m^{1-\alpha} k^2, with \alpha = (4-d)/2 (2<d<4) for disordered systems, and \alpha = (3-d) (1<d<3) for clean ones. In d=4 (disordered) and d=3 (clean), \Omega ~ m ln(1/m) k^2. Experiments to test these predictions are proposed.Comment: 4 pp., REVTeX, no fig

Properties of spin-triplet, even-parity superconductors

The physical consequences of the spin-triplet, even-parity pairing that has been predicted to exist in disordered two-dimensional electron systems are considered in detail. We show that the presence of an attractive interaction in the particle-particle spin-triplet channel leads to an instability of the normal metal that competes with the localizing effects of the disorder. The instability is characterized by a diverging length scale, and has all of the characteristics of a continuous phase transition. The transition and the properties of the ordered phase are studied in mean-field theory, and by taking into account Gaussian fluctuations. We find that the ordered phase is indeed a superconductor with an ordinary Meissner effect and a free energy that is lower than that of the normal metal. Various technical points that have given rise to confusion in connection with this and other manifestations of odd-gap superconductivity are also discussed.Comment: 15 pp., REVTeX, psfig, 2 ps figs, final version as publishe

Nature of the Quantum Phase Transition in Clean, Itinerant Heisenberg Ferromagnets

A comprehensive theory of the quantum phase transition in clean, itinerant Heisenberg ferromagnets is presented. It is shown that the standard mean-field description of the transition is invalid in spatial dimensions $d\leq 3$ due to the existence of soft particle-hole excitations that couple to the order parameter fluctuations and lead to an upper critical dimension $d_c^+ = 3$. A generalized mean-field theory that takes these additional modes into account predicts a fluctuation-induced first-order transition. In a certain parameter regime, this first-order transition in turn is unstable with respect to a fluctuation-induced second-order transition. The quantum ferromagnetic transition may thus be either of first or of second-order, in agreement with experimental observations. A detailed discussion is given of the stability of the first-order transition, and of the critical behavior at the fluctuation-induced second-order transition. In $d=3$, the latter is mean field-like with logarithmic corrections to scaling, and in $d<3$ it can be controlled by means of a $3-\epsilon$ expansion.Comment: 15 pp., revtex4, 6 eps figs; final version as publishe