First principles Study on Transparent High-Tc Superconductivity in hole-doped Delafossite CuAlO2

The CuAlO$_2$ is the transparent $p$-type conductor without any intentional doping. Transparent superdoncutivity and high thermoelectric power are suggested in $p$-type CuAlO$_2$ [1]. Katayama-Yoshida {\it et al.} proposed that it may cause a strong electron-phonon interaction and a superconductivity. But, the calculation of superconducting critical temperature $T_{\rm c}$ is not performed. We performed the first principles calculation about the $T_{\rm c}$ of hole-doped CuAlO$_2$ by shifting the Fermi level rigidly. In lightly hole-doped CuAlO$_2$, the Fermi level is located at Cu and O anti-bonding band. The electrons of this band strongly interact with the A$_1$L$_1$ phonon mode because the direction of O-Cu-O dumbbell is parallel to the oscillation direction of the A$_1$L$_1$ phonon mode. As a result, $T_{\rm c}$ of lightly hole-doped CuAlO$_2$ is about 50 K. We also discuss the materials design to enhance the $T_{\rm c}$ based on the charge-excitation-induced negative effective $U$ system.\\[4pt] [1] H. Katayama-Yoshida, T. Koyanagi, H. Funashima, H. Harima, A. Yanase: Solid State Communication {\bf 126} (2003) 135. \\[0pt] [2] A. Nakanishi and H. Katayama-Yoshida: Solid State Communication, in printing. (arXiv:1107.2477v3