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.

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