Phenomenological theory of the underdoped phase of a high-Tc superconductor

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We model the Fermi surface of the cuprates by one-dimensional nested parts near (0,π) and (π,0) and unnested parts near the zone diagonals. Fermions in the nested regions form 1D spin liquids, and develop spectral gaps below some T*, but superconducting order is prevented by 1D phase fluctuations. We show that the Josephson coupling between order parameters at (0,π) and (π,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 Tc < T**, at which the system develops a (quasi-) long-range superconducting order.