Stability of the spiral phase and superconductivityin the two-dimensional t-J model

We analyse the t-t′-t″-J model, relevant to the superconducting cuprates. By using chiral perturbation theory we have determined the ground state to be a spiral for small doping δ≪1 near half filling. At t′=t″=0 the spiral state is unstable towards a local enhancement of the spiral pitch, and the nature of the true ground state remains unclear. However, for values of t′ and t″ corresponding to real cuprates the (1,0) spiral state is stabilized by spin quantum fluctuations ('order from disorder' effect). We show that at δ≈0.119 the spiral is commensurate with the lattice with a period of 8 lattice spacings. It is also demonstrated that spin-wave mediated superconductivity develops in the spiral state [O.P. Sushkov, V.N. Kotov, Phys. Rev. B 70, (2004) 024503; V.N. Kotov, O.P. Sushkov, Phys. Rev. B 70 (2004) 195105].