Superconductivity in a Toy Model of the Pseudogap State

TL;DR

This paper presents an exactly solvable model showing that superconductivity can exist locally above the critical temperature in pseudogap states, aligning with experimental observations in underdoped cuprates.

Contribution

It introduces a simple solvable model demonstrating local superconductivity above T_c in pseudogap states, highlighting the role of short-range order fluctuations.

Findings

Superconducting gap persists above T_c in the model.

Superconductivity signals appear in spectral density and density of states above T_c.

Model results qualitatively match experimental data on underdoped cuprates.

Abstract

We analyze superconducting state (both s and d - wave) in a simple exactly solvable model of pseudogap state, induced by short - range order fluctuations (e.g. antiferromagnetic), which is based upon model Fermi - surface with "hot patches". It is shown that superconducting energy gap averaged over these fluctuations is non zero even for the temperatures larger than mean - field T_c of superconducting transition in a sample as a whole. For temperatures T>T_c superconductivity apparently exists within separate regions ("drops"). We study the spectral density and the density of states and demonstrate that superconductivity signals itself in these already for T>T_c, while at T_c itself nothing special happens from this point of view. These anomalies are in qualitative agreement with a number experiments on underdoped cuprates.