Slope of $H_{c2}$ close to $T_c$ versus the size of the Cooper pairs: The role of disorder in Dynes superconductors

Abstract

The size of the Cooper pair ${\xi }_{\mathrm{pair}}$ is one of the basic characteristics of a superconductor, but it is not possible to measure it directly. It might be argued that ${\xi }_{\mathrm{pair}}$ can be determined from the value ${\xi }_{\mathrm{slope}}$ extracted from the measurement of the slope of $H_{c2}$ close to $T_c$. Taking into account both pair-conserving and pair-breaking scattering on impurities within the recently developed theory of Dynes superconductors, we perform an explicit calculation of ${\xi }_{\mathrm{pair}}$ and ${\xi }_{\mathrm{slope}}$. We show that the two quantities agree only in clean superconductors. In particular, when the pair-breaking disorder approaches the quantum critical point, ${\xi }_{\mathrm{pair}}$ stays finite, whereas ${\xi }_{\mathrm{slope}}$ diverges.

6 pages, 3 figures