Superconductivity in a quasi-one-dimensional spin liquid.

The single rung t-J ladder is analyzed in a mean field theory using Gutzwiller renormalization of the matrix elements to account for strong correlation. The spin liquid (RVB) state at half-filling evolves into a superconducting state upon doping. The order parameter has a modified d-wave character. A lattice of weakly coupled ladders should show a superconducting phase transition. PACS: 71.27.+a, 74.20.Mn, 75.10.Jm There is a striking difference between the properties of a chain and a ladder (double chain) antiferromagnetic (AF) s=1/2 Heisenberg model. Whereas the chain has power law decay of the AF-correlations, the ladder has a purely exponential decay and a finite energy gap in the spin excitation spectrum, i.e. a spin gap (see for example Ref.1). If, as is the case for other spin gap systems, the spin gap persists to finite doping, then the possibilities for superconducting fluctuations are greatly enhanced in ladder systems [2]. Recently we pointed out that the compound Sr2Cu4O6 offers the possibility of realizing a lattice of weakly coupled ladders [3,4].