Electromagnetic response of superconductors and optical sum rule
A.E. Karakozov (L.F. Vereshchagin Institute for High Pressure Physics,, RAS, Troitsk, Moscow region, Russia), E.G. Maksimov (P.N. Lebedev Physical, Institute, Moscow, Russia), and O.V. Dolgov (Max-Planck-Institut fuer, Festkoerperforschung, Stuttgart, Germany)

TL;DR
This paper investigates how the optical sum rule relates to superconductivity, showing that observed violations are mainly due to temperature-dependent relaxation rates and can be explained by strong electron-phonon interactions.
Contribution
It clarifies the origin of partial sum rule violations and demonstrates the role of electron-phonon interactions in the optical properties of superconductors.
Findings
Partial sum rule violation is mainly due to temperature-dependent relaxation rates.
Strong electron-phonon interaction explains the temperature dependence of the optical sum rule.
Experimental data aligns well with the theoretical model considering electron-phonon effects.
Abstract
The interrelation between the condensation energy and the optical sum rules has been investigated. It has been shown that the so called 'partial' sum rule violation is related mainly to a temperature dependence of the relaxation rate rather than to the appearance of superconductivity itself. Moreover, we demonstrate that the experimental data on the temperature dependence of the optical sum rule can be explained rather well by an account of strong electron-phonon interaction.
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