Universal Scaling Law for the Condensation Energy, U, Across a Broad Range of Superconductor Classes

TL;DR

This study reveals a universal scaling law for the superconducting condensation energy across diverse superconductor classes, linking it to critical temperature and specific heat, thus unifying understanding of their energetic behaviors.

Contribution

The paper uncovers a universal U/gamma scaling law for superconductors, bridging weak and strong coupling regimes across multiple classes.

Findings

U scales with Tc as U=0.1Tc^{3.4} in IBS and BCS superconductors.

Heavy Fermion superconductors show a significantly enhanced U compared to IBS/BCS.

All investigated superconductors follow a universal U/gamma=0.2Tc^{2} dependence.

Abstract

One of the goals in understanding any new class of superconductors is to search for commonalities with other known superconductors. The present work investigates the superconducting condensation energy, U, in the iron based superconductors (IBS), and compares their U with a broad range of other distinct classes of superconductor, including conventional BCS elements and compounds and the unconventional heavy Fermion, Sr2RuO4, Li0.1ZrNCl, kappa-(BEDT-TTF)2Cu(NCS)2 and optimally doped cuprate superconductors. Surprisingly, both the magnitude and Tc dependence (U=0.1Tc**3.4 +- 0.2) of U are, contrary to the previously observed behavior of the specific heat discontinuity at Tc, deltaC, quite similar in the IBS and BCS materials for Tc>1.4 K. In contrast, the heavy Fermion superconductors U vs Tc are strongly (up to a factor of 100) enhanced above the IBS/BCS while the cuprate superconductors U are strongly (factor of 8) reduced. However, scaling of U with the specific heat gamma (or deltaC) brings all the superconductors investigated onto one universal dependence upon Tc. This apparent universal scaling U/gamma = 0.2Tc**2 for all superconductor classes investigated, both weak and strong coupled and both conventional and unconventional, links together extremely disparate behaviors over almost seven orders of magnitude for U and almost three orders of magnitude for Tc. Since U has not yet been explicitly calculated beyond the weak coupling limit, the present results can help direct theoretical efforts into the medium and strong coupling regimes.