Chemical Trend of Superconducting Transition Temperature in Hole-doped CuBO${}_2$, CuAlO${}_2$, CuGaO${}_2$ and CuInO${}_2$

We calculated the superconducting transition temperature $T_{\mathrm{c}}$ of hole-doped CuBO${}_2$, CuAlO${}_2$, CuGaO${}_2$ and CuInO${}_2$ using first-principles. The calculated $T_{\mathrm{c}}$ are about 50 K for CuAlO${}_2$, 10 K for CuBO${}_2$ and CuGaO${}_2$ and 1 K for CuInO${}_2$ at maximum in the optimum hole-doping concentration. The low $T_{\mathrm{c}}$ of CuInO${}_2$ is attributed to the weak electron-phonon interaction caused by the low covalency and heavy atomic mass.