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

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 these order parameters locks their relative phase at π at the 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.