Phase-fluctuation-induced reduction of the kinetic energy at the superconducting transition

Recent reflectivity measurements indicated a possible violation of the in-plane optical integral in the underdoped high-T-c compound Bi2Sr2CaCu2O8+delta up to frequencies much higher than expected by the standard BCS theory. The sum rule violation may be related to a loss of in-plane kinetic energy at the superconducting transition. Here, we show that a model based on phase fluctuations of the superconducting order parameter introduces a change of the in-plane kinetic energy at T-c. The change is due to a transition from a phase-incoherent Cooper-pair motion in the pseudogap regime above T-c to a phase-coherent motion at T-c.