Spectral Anomaly and High Temperature Superconductors

TL;DR

This paper investigates spectral anomalies in interacting Fermions, introduces a new class with specific scaling exponents, and explores how attractive interactions induce a novel superconducting state relevant to high-temperature cuprates.

Contribution

It presents a detailed example of spectral scaling with anomalous exponents and analyzes how attractive interactions lead to a new superconducting phase.

Findings

Identification of a new spectral scaling class with specific exponents

Demonstration of how attractive interactions induce superconductivity in this class

Discussion of relevance to high-temperature cuprate 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.