d-wave superconductivity in coupled ladders

We study the one-band Hubbard model on the trellis lattice, a two-dimensional frustrated lattice of coupled two-leg ladders, with hopping amplitude t within ladders and t' between ladders. For large U/t this is a model for the cuprate Sr14-x CaxCu24O41. We investigate the phase diagram as a function of doping for U = 10t using two quantum cluster methods: The variational cluster approximation (VCA), with clusters of sizes 8 and 12, and cellular dynamical mean field theory (CDMFT), both at zero temperature. Both methods predict a superconducting dome, ending at roughly 20% doping in VCA and 15% in CDMFT. In VCA, the superconducting order parameter is complex in a range of doping centered around 10%, corresponding to bulk chiral, T -violating superconductivity. However, the CDMFT solution is not chiral. We find evidence for a migration of the Cooper pairs from the interladder region towards the plaquettes as doping is increased.