# Competition Between Spin Density Wave Order and Superconductivity in the Underdoped Cuprates

 Title: Competition Between Spin Density Wave Order and Superconductivity in the Underdoped Cuprates Author: Moon, Eun; Sachdev, Subir Note: Order does not necessarily reflect citation order of authors. Citation: Moon, Eun, and Subir Sachdev. 2009. Competition between spin density wave order and superconductivity in the underdoped cuprates. Physical Review B 80(3): 035117. Full Text & Related Files: 0905.2608v3.pdf (354.5Kb; PDF) 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. Phys. Rev. Lett. 87 067202 (2001)] 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. Published Version: doi://10.1103/PhysRevB.80.035117 Other Sources: http://arxiv.org/abs/0905.2608v3 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:7408618

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