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A Consistent Theory of Underdoped Cuprates: Evolution of the RVB State From Half Filling

We have been able to resolve two long-standing issues that are central to the theory of high Tc superconductivity: (1) How is the physics of the doped region connected to that of the Mott insulator? (2) What is the origin of the two-dimensionality of the normal state? Specifically, based on the t-J model, we derive a renormalized Hamiltonian to describe the properties of underdoped cuprates. The theory is constrained to agree with the behavior at half filling, which is well described by the bosonic RVB state of Arovas and Auerbach. Moving holes are assumed to destroy long-range magnetic order, which leads to a gap in the spinon spectrum. The presence of the spin gap allows us to derive a constrained Hamiltonian which describes sublattice-preserving hopping by renormalized holons and holon pairs, accompanied by spinon singlet backflows. Below the singlet condensation, i.e, the psudogap (as distinct from the spin gap), temperature T*, holons form a spinless Fermi liquid without an observable small Fermi surface. Above T* holons are localized, giving rise to a (gauge) insulator, which we identify with the strange metal phase. Holon pair hopping leads to a robust d-wave superconductor, its symmetry determined primarily by the symmetry of the RVB state at half filling. The predictions of the theory are shown to be consistent with the results of nmr, tunneling and transport experiments. Remarkably, the existence of the spin gap provides a natural explanation for the two-dimensionality of the normal state. The marked asymmetry between hole-doped and electron-doped cuprates is also easily explained.