Nodeless $s$-Wave Superconducting Phases in Cuprates with Ba$_2$CuO$_3$-Type Structure

In this work zero-temperature phase diagrams of cuprates with Ba$_2$CuO$_3$-type CuO chain structure is investigated. The projective symmetry group analysis is employed in the strong coupling limit, and renormalization group with bosonization analysis is employed in the weak coupling limit. We find that in both of these two limits, large areas of the phase diagrams are filled with nodeless $s$-wave superconducting phases (with weak $d$-wave components), instead of pure $d$-wave phase mostly found in cuprates. This implies that nodeless $s$-wave phase is the dominant superconducting phase in cuprates with Ba$_2$CuO$_3$-type CuO chain structure in low temperature. Other phases are also found, including $(s+d)$-wave superconducting phases and Luttinger liquid phases.