Spectral Anomaly and High Temperature Superconductors

Spectral anomaly for interacting fermions is characterized by the spectral function A ([k − k F ], ω) satisfying the scaling relation A (Λ y 1 [k − k F ], Λ y 2 ω) =Λ y A A ([k − k F ], ω), where y 1 , y 2 , and y A are the exponents defining the universality class. For a Fermi liquid y 1 = 1, y 2 = 1, y A = −1; all other values of the exponents are termed anomalous. In this paper, an example for which y 1 = 1, y 2 = 1, but y A = α − 1 is considered in detail. Attractive interaction added to such a critical system leads to a novel superconducting state, which is explored and its relevance to high temperature cuprate superconductors is discussed.