Phenomenological theory of the underdoped phase of a high-T$_c$ superconductor

TL;DR

This paper presents a phenomenological model of underdoped cuprates, describing how nested and unnested Fermi surface regions interact to produce pseudogap behavior and eventual superconductivity through phase locking and dimensional crossover.

Contribution

It introduces a model combining nested and unnested Fermi surface parts to explain the pseudogap and superconducting transition in high-Tc cuprates, emphasizing phase fluctuations and Josephson coupling effects.

Findings

Spectral gaps form below T* in nested regions.

Phase locking at T** leads to 2D response and Nernst effect.

Superconducting order develops at Tc with phase coherence.

Abstract

We model the Fermi surface of the cuprates by one-dimensional nested parts near $(0,\pi)$ and $(\pi,0)$ and unnested parts near the zone diagonals. Fermions in the nested regions form 1D spin liquids, and develop spectral gaps below some $\sim T^*$, but superconducting order is prevented by 1D phase fluctuations. We show that the Josephson coupling between order parameters at $(0,\pi)$ and $(\pi,0)$ locks their relative phase at a crossover scale $T^{**}< T^*$. Below $T^{**}$, the system response becomes two-dimensional, and the system displays Nernst effect. The remaining total phase gets locked at $T_c < T^{**}$, at which the system develops a (quasi-) long-range superconducting order.