Thermodynamics of strong coupling superconductors including the effect of anisotropy

Abstract

The thermodynamics of several elemental superconductors is computed from isotropic Eliashberg theory formulated on the imaginary frequency axis. A symmary of the available experimental literature is presented and a comparison with theory is given. The small disagreements that are found are all in the direction expected from anisotropy effects. We calculate the effect of a small amount of model anisotropy on the critical temperature, critical field, and high-temperature specific heat from an exact solution of the anisotropic Eliashberg equations. These are the first such results below the critical temperature ; unlike previous analytical work, we include retardation, anisotropy in the mass enhancement, and the effect of the Coulomb repulsion in enhancing anisotropy, all of which are significant. We derive a new formula independent of any model anisotropy for the rate of decrease with impurity lifetime of the critical temperature. Finally we demonstrate how the commonly used formulas of Markowitz and Kadanoff and of Clem may give entirely misleading estimates of the gap anisotropy when used to interpret certain experiments.

Renormalization group approach to anisotropic superconductivity

“…The set of equations derived here reduce to those given by earlier treatment of Eliashberg theory for anisotropic electron-boson interaction by Daams and Carbotte, 42 if we consider a single separable channel ␥ = 1 and n =1.…”

Lower critical field and magnetization of strong-coupling, type II superconductors in the dirty limit

“…25" 26 We have solved the system of Eqs. (1), (4), (5), and (8) with the boundary conditions (9), (10).…”

Heat capacity of tantalum in the normal and superconducting states: Identification of the contributions

“…) falls in the range from 3.33 ± 0.05 [20] to 7.83 [19]; in most works, its values lie in the range 5 ≤ ζ ≤ 7. In other words, there is no generally accepted value of ζ.…”

“…Unfortunately, good agreement between the results of such calculations and experimental data was only obtained in a few cases for some properties in limited temperature and pressure ranges. In particular, it is difficult to calculate the heat capacity of tantalum C(T) and the derivative proper ties, namely, Debye temperature θ D (T) and electronic heat capacity coefficient ζ [9][10][11][12][13][14][15][16][17][18][19][20]. However, it is these properties that substantially determine the change in the thermodynamic properties of tantalum at interme diate and high temperatures.…”

“…First, tantalum is a supercon ductor with a rather high superconducting transition temperature T sc = 4.39 K; from this standpoint, it is a [17,19,20]). Tan talum is considered to be a simple superconductor, and a change in it thermodynamic properties is well described by the Bardeen-Cooper-Schrieffer (BCS) theory [26].…”