Phenomenological theory of the pseudogap state

An ansatz is proposed for the coherent part of the single particle Green's function in a doped resonant valence bond (RVB) state by analogy with the form derived by Konik and co-workers for a doped spin liquid formed by an array of two-leg Hubbard ladders near half-filling. The parameters of the RVB state are taken from the renormalized mean field theory of Zhang and co-workers for underdoped cuprates. The ansatz shows good agreement with recent angle resolved photoemission on underdoped cuprates and resolves an apparent disagreement with the Luttinger sum rule. The transition in the normal state from a doped RVB spin liquid to a standard Landau Fermi liquid, that occurs in the renormalized mean field theory, appears as a quantum critical point characterized by a change in the analytic form of the Green's function. A d-wave superconducting dome surrounding this quantum critical point is introduced phenomenologically. Results are also presented for the Drude weight and tunneling density of states as functions of the hole density.