Impact of a finite cut-off for the optical sum rule in the superconducting state

TL;DR

This paper investigates how truncating the optical sum rule at finite frequencies affects interpretations of superconducting states, revealing that such truncations can exaggerate observed anomalies and influence the understanding of kinetic energy-driven superconductivity.

Contribution

It provides a theoretical analysis of the effects of finite frequency cutoffs on the optical sum rule in superconductors, clarifying their impact on experimental interpretations.

Findings

Finite cutoffs can amplify the observed temperature dependence in superconducting states.

Normal state temperature dependence can be largely attributed to cutoff effects.

Proper accounting for cutoffs shows the anomalous behavior is more pronounced than previously thought.

Abstract

A single band optical sum rule derived by Kubo can reveal a novel kind of superconducting state. It relies, however, on a knowledge of the single band contribution from zero to infinite frequency. A number of experiments over the past five years have used this sum rule; their data has been interpreted in support of 'kinetic energy-driven superconductivity'. However, because of the presence of unwanted interband optical spectral weight, they necessarily have to truncate their sum at a finite frequency. This work examines theoretical models where the impact of this truncation can be examined first in the normal state, and then in the superconducting state. The latter case is particularly important as previous considerations attributed the observed anomalous temperature dependence as an artifact of a non-infinite cutoff frequency. We find that this is in fact not the case, and that the sign of the corrections from the use of a non-infinite cutoff is such that the observed temperature dependence is even more anomalous when proper account is taken of the cutoff. On the other hand, in these same models, we find that the strong observed temperature dependence in the normal state can be attributed to the effect of a non-infinite cutoff frequency.