Cuprates intermediate between one and two dimensions

The key elements in all known cuprate superconductors are lightly doped CuO_i-planes. Recently a new homologous series of compounds Sr_n–1Cu_n+1O_2n have been reported in which the planes contain a parallel array of line defects which form a trellis lattice with ladder-segments of the square lattice weakly coupled through triangular line defects. The width of the ladder segments is determined by the parameter n and varies from single chains to arbitrarily wide ladders. The magnetic properties of undoped compounds will be dominated by the properties of the ladders. Heisenberg s = 1/2 ladders can have a spin liquid groundstate with a spin gap if the number of rungs is odd so that a short range RVB groundstate is predicted for such trellis lattices. Using a t-J model to describe the doped material leads to the prediction of a d-wave RVB superconducting groundstate with a large spin gap.