Spectral anomaly and high temperature superconductors

Spectral anomaly for interacting fermions is characterized by the spectral function A([k-k(F)],omega) satisfying the scaling relation A(Lambda(y1)[k-k(F)],Lambda(y2)omega) = Lambda(yA)A([k-k(F)],omega), 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) = alpha-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.