Competition between spin density wave order and superconductivity in the underdoped cuprates

TL;DR

This paper develops a theoretical framework to understand the competition between spin density wave order and d-wave superconductivity in underdoped cuprates, explaining phase diagram features and the stability of magnetic order.

Contribution

It introduces a minimal universal theory capturing the interplay of SDW order and superconductivity, including quantum fluctuations and phase diagram predictions.

Findings

Superconductivity enhances the stability of SDW order in the metallic state.

The theory reproduces key features of the cuprate phase diagram.

Superconductivity shifts the SDW quantum critical point to lower doping.

Abstract

We describe the interplay between d-wave superconductivity and spin density wave (SDW) order in a theory of the hole-doped cuprates at hole densities below optimal doping. The theory assumes local SDW order, and associated electron and hole pocket Fermi surfaces of charge carriers in the normal state. We describe quantum and thermal fluctuations in the orientation of the local SDW order, which lead to d-wave superconductivity: we compute the superconducting critical temperature and magnetic field in a `minimal' universal theory. We also describe the back-action of the superconductivity on the SDW order, showing that SDW order is more stable in the metal. Our results capture key aspects of the phase diagram of Demler et al. (cond-mat/0103192) obtained in a phenomenological quantum theory of competing orders. Finally, we propose a finite temperature crossover phase diagram for the cuprates. In the metallic state, these are controlled by a `hidden' quantum critical point near optimal doping involving the onset of SDW order in a metal. However, the onset of superconductivity results in a decrease in stability of the SDW order, and consequently the actual SDW quantum critical point appears at a significantly lower doping. All our analysis is placed in the context of recent experimental results.