Non-BCS behavior of optical properties across the cuprate phase diagram

The finite-frequency optical properties of the underdoped cuprates, in both the normal and superconducting state, display features which go beyond a Fermi liquid and a BCS description. We provide an understanding of these properties within a simplified analytical model, which has been evolved out of the Hubbard model and ideas based on a resonating valence bond spin liquid. We find that: 1) in underdoped samples, the missing area integrals reveal a second energy scale due to the pseudogap, not present at optimum or overdoping; 2) the real part of the optical self-energy shows a large sharp peak, that emerges with the opening of the pseudogap which exists within the superconducting state and persists in the normal state; and 3) the amount of optical spectral weight which is transferred to the condensate is greatly reduced by the presence of the pseudogap as compared to the Fermi liquid case. These non-BCS features of the superconducting state are in good qualitative agreement with a body of experimental work on different cuprate systems and provide strong evidence from optical conductivity that they are all a manifestation of the pseudogap energy scale.