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A single band optical sum rule derived by Kubo can reveal a novel kind ofsuperconducting state. It relies, however, on a knowledge of the single bandcontribution from zero to infinite frequency. A number of experiments over thepast five years have used this sum rule; their data has been interpreted insupport of 'kinetic energy-driven superconductivity'. However, because of thepresence of unwanted interband optical spectral weight, they necessarily haveto truncate their sum at a finite frequency. This work examines theoreticalmodels where the impact of this truncation can be examined first in the normalstate, and then in the superconducting state. The latter case is particularlyimportant as previous considerations attributed the observed anomaloustemperature dependence as an artifact of a non-infinite cutoff frequency. Wefind that this is in fact not the case, and that the sign of the correctionsfrom the use of a non-infinite cutoff is such that the observed temperaturedependence 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 observedtemperature dependence in the normal state can be attributed to the effect of anon-infinite cutoff frequency.

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