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In this work zero-temperature phase diagrams of cuprates withBa$_2$CuO$_3$-type CuO chain structure is investigated. The projective symmetrygroup analysis is employed in the strong coupling limit, and renormalizationgroup with bosonization analysis is employed in the weak coupling limit. Wefind that in both of these two limits, large areas of the phase diagrams arefilled with nodeless $s$-wave superconducting phases (with weak $d$-wavecomponents), instead of pure $d$-wave phase mostly found in cuprates. Thisimplies that nodeless $s$-wave phase is the dominant superconducting phase incuprates with Ba$_2$CuO$_3$-type CuO chain structure in low temperature. Otherphases are also found, including $(s+d)$-wave superconducting phases andLuttinger liquid phases.

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