Thermodynamics of Eliashberg theory in the weak-coupling limit

Abstract

The weak-coupling limits of the gap and critical temperature computed within Eliashberg theory surprisingly deviate from the BCS theory predictions by a factor of $1/\sqrt{e}$. Interestingly, however, the ratio of these two quantities agrees for both theories. Motivated by this result, here we investigate the weak-coupling thermodynamics of Eliashberg theory, with a central focus on the free energy, specific heat, and the critical magnetic field. In particular, we numerically calculate the difference between the superconducting and normal-state specific heats, and we find that this quantity differs from its BCS counterpart by a factor of $1/\sqrt{e}$, for all temperatures below $T_c$. We find that the dimensionless ratio of the specific-heat discontinuity to the normal-state specific heat reduces to the BCS prediction given by $\Delta C_V(T_c)/C_{V,n}(T_c)\approx 1.43$. This gives further evidence to the expectation that all dimensionless ratios tend to their "universal values" in the weak-coupling limit.

arXiv comment6 pages, 5 figures

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Cited by in corpus (4)

• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. I: The $\gamma$-model and its phase diagram at $T=0$. The case $0<\gamma <1$
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal: V. The $\gamma$ model and its phase diagram. The case $\gamma =2$
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. III: The $\gamma$ model and its phase diagram across $\gamma =1$
• Electrical conductivity and nuclear magnetic resonance relaxation rate of Eliashberg superconductors in the weak-coupling limit