Mode propagation in superconductors near T/sub c/

Journal Article · Tue Oct 31 23:00:00 EST 1978 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(78)90003-9· OSTI ID:6319808

Entin-Wohlman, O; Orbach, R

The linearized Eliashberg theory for dirty superconductors in the vicinity of T/sub c/ is used to generate the dynamic Ginzburg--Landau (GL) equation for the order parameter and the coupled Boltzmann equation for the quasi-particle distribution function, with and without magnetic impurities and inelastic phonon scattering. The Schmid and Schoen (SS) separation of the order parameter into longitudinal (real) and transverse (imaginary) components is shown to be exact to linear order. Explicit expressions are exhibited for the current and charge densities to leading order (..delta../T in the gap regime, in which ..delta../sub taus/>1 where tau/sub s/ is the conduction electron spin flip lifetime; and ..delta../sup 2//T (..omega..+iDk/sup 2/) in gapless regime; ..delta../sub taus/<1. D is the diffusion constant). The continuity equation is shown to be obeyed to this order.Use of the Poisson equation in relation to the transverse component leads to a propagating mode, which, in the absence of magnetic impurities, reduces to the SS result. The mode propagates only in the gap regime, whereas it is purely diffusive in the gapless regime and for gapless superconductors. In the presence of magnetic impurities, the solution reduces to the SS limit. The charge density appropriate to the propagating mode is shown to be zero to order ..omega../..omega../sub rho//sup 2/tau/sub 1/, where tau/sub 1/ is the impurity scattering time and ..omega../sub rho/ the plasma frequency. The characteristic penetration length of an electric field into a superconductor is calculated, taking into account the phonon inelastic scattering time. The result reproduces the Waldram and SS expressions. The characteristic penetration length is also obtained in the gapless regime and for gapless superconductors for which T/sub c/tau/sub s/>1.Finally, the longitudinal and transverse pair susceptibilities are calculated with and without magnetic impurities and in the gap and gapless regimes.

• Research Organization: Physics Department, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel
• OSTI ID: 6319808
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 115:1; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

656101* -- Solid State Physics-- Superconductivity-- General Theory-- (-1987)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOLTZMANN EQUATION
CONTINUITY EQUATIONS
DATA
DATA FORMS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
EQUATIONS
FUNCTIONS
GINZBURG-LANDAU THEORY
GORKOV-ELIASHBERG THEORY
GREEN FUNCTION
INFORMATION
ISOLATED VALUES
NUMERICAL DATA
ORDER PARAMETERS
PHONONS
PHYSICAL PROPERTIES
POISSON EQUATION
QUASI PARTICLES
SUPERCONDUCTORS
THEORETICAL DATA
THERMODYNAMIC PROPERTIES
TRANSITION TEMPERATURE
WAVE PROPAGATION