Abstract
A mechanism is proposed for the pairing of holes in the resonating-valence-bond (RVB) state for two-dimensional alternate lattices such as found in copper oxide high-${T}_{c}$ materials. The main ingredients of the attractive force are the kinetic motion of holes which in fact stabilizes the RVB state and the topological and statistical nature of the RVB state. The size of a pair of holes is the order of the antiferromagnetic correlation length. A schematic phase diagram in terms of the concentration of holes and temperature is drawn which includes a paramagnetic phase, an antiferromagnetic phase, two types of spin-liquid phases, and a superconducting phase.
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