Spectral Anomaly and High Temperature Superconductors

Abstract

Spectral anomaly for interacting Fermions is characterized by the spectral function $A([k-k_F],\omega )$ satisfying the scaling relation $A({\Lambda }^{y_1}[k-k_F],{\Lambda }^{y_2}\omega )={\Lambda }^{y_A}A([k-k_F],\omega )$, 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.

RevTex, 53 pages (including figures)

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