Pairing-induced kinetic energy lowering in doped antiferromagnets

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We analyse lowering of the kinetic energy in doped antiferromagnets at the transition to thesuperconducting state. Measurements of optical conductivity indicate that suchunconventional behaviour takes place in underdoped Bi-2212. We argue thatthe definition of the operator representing the kinetic energy is determined byexperimental conditions. The thermodynamic average of that operator is related to theintegrated spectral weight of the optical conductivity and thus depends on the cut-offfrequency limiting that integral. If the upper limit of the integral lies below thecharge transfer gap the spectral weight represents the average of the hoppingterm in the space restricted to the energy range below the gap. We show thatthe kinetic energy is indeed lowered at the superconducting transition in thet–J model(tJM),which is an effective model defined in the restricted space. That result is in agreement withexperimental observations and may be attributed to the formation of spin polarons and thechange of roles which are played by the kinetic and the potential energy in thetJM and in some effective model for spin polarons. The total spectral weight represents thekinetic energy in a model defined in a broader space if the upper limit in the integral of theoptical conductivity is set above the gap. We demonstrate that the kinetic energy in theHubbard model is also lowered in the superconducting state. That result doesnot agree with experimental observations, indicating that the spectral weight isconserved for all temperatures if the upper limit of the integral is set above thecharge transfer gap. This discrepancy suggests that a single band model is notcapable of describing in some respects the physics of excitations across the gap.