Oscillator-Strength Sum Rule in the Cuprates

Abstract

The oscillator-strength sum rule played an important role in the firstwork on the energy gap of superconductors by Tinkham. Recently, asmall but measurable depletion in the sum rule integral has beenobserved at optical frequencies in the cuprates. It has been suggestedthat this behavior contradicts what is expected of traditional modelsof superconductivity. We disagree with this conclusion. We show thatthis depletion is consistent with earlier Thermal DifferenceReflectance (TDR) measurements and their interpretation within thestrong coupling extension of the BCS theory, as evidence of anelectronic contribution to the pairing interaction at energies between1.0 and 2.0 eV for these materials. We show quantitative agreementwith the magnitude of the depletion and agreement with recent workwith ARPES on the dispersion and lifetime of quasiparticles from thesame model. We have located the two transitions responsible for theelectronic contribution from TDR measurements of the thermalderivative of the dielectric function.