Non-Bardeen-Cooper-Schrieffer behavior of optical properties across the phase diagram of cuprate superconductors

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Abstract
The finite-frequency optical properties of the underdoped cuprates, in both the normal and superconducting states, display features which go beyond a Fermi liquid and a Bardeen-Cooper-Schrieffer (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.
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