The effect of RVB flux configuration on the superconducting state

The RVB state is a singlet quantum liquid which can support periodic or fluid-like quantum circulation around the elementary plaquette in two dimensions. In the s + id phase there is a half flux quanta of circulation in every elementary plaquette. The authors show that the holons in the presence of this lattice of circulation have a two-valley structure, as opposed to s or d states, which have a single valley. Using an effective holon Hamiltonian, they study the mean-field properties of the two-valley holon condensate, and compare its energy with the single valley case. A transition from the d to the s +id state is predicted with increasing hole concentration for sufficiently large Hubbard U. Some speculations are offered about the general case of a fluid-like distribution of flux quanta