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

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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.