Quasiparticle Formation and Optical Sum Rule Violation in Cuprate   Superconductors
  Using a simple model for the frequency dependent scattering rate, we evaluate the in-plane optical integral for cuprate superconductors in the normal and superconducting states. In the overdoped region, this integral is conserved. In the optimal and underdoped region, though, the optical integrals differ, implying a lowering of the in-plane kinetic energy in the superconducting state. This sum rule violation, due to the difference of the non Fermi liquid normal state and the superconducting Fermi liquid state, has a magnitude comparable to recent experimental results. 
M. R. Norman, C. Pepin