Abstract
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 ${t}^{\ensuremath{'}}$ between ladders. For large $U/t$ this is a model for the cuprate ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$. 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.
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