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In order to realize super-high-critical temperature $(T_c)$ superconductors($T_c$>1,000 K) based on general design rules for negative effective $U$$(U_{eff})$ systems by controlling purely-electronic and attractive Fermionmechanisms, we perform computational materials design for the negative$U_{eff}$ system in hole-doped two-dimensional (2D) Delafossite CuAlO$_2$,AgAlO$_2$ and AuAlO$_2$ from ${\it ab\ initio}$ calculations. It is found thatthe large negative $U_{eff}$ in the hole-doped attractive Fermion systems forCuAlO$_2$ ($U_{eff}$ = -4.53 eV), AgAlO$_2$ ($U_{eff}$ = -4.88 eV), AuAlO$_2$($U_{eff}$ = -4.14 eV). These values are 10 times larger than that inhole-doped three-dimensional (3D) CuFeS$_2$ ($U_{eff}$ = -0.44 eV). For futurecalculations of the $T_c$ and phase diagram by quantum Monte Carlo simulations,we propose the negative $U_{eff}$ Hubbard model with the anti-bonding single$\pi$-band model for CuAlO$_2$, AgAlO$_2$ and AuAlO$_2$ by using the parametersobtained from ${\it ab\ initio}$ electronic structure calculations. Thebehavior of $T_c$ in the 2D Delafossite of CuAlO$_2$, AgAlO$_2$ and AuAlO$_2$and 3D Chalcopyrite of CuFeS$_2$ shows the interesting chemical trend, ${\iti.e.,}$ $T_c$ increases exponentially in the weak coupling regime $|U_{eff}| <W$ ($\sim$ 2 eV) (where $W$ is the band width of Hubbard model) for thehole-doped CuFeS$_2$, and then $T_c$ goes through a maximum when $|U_{eff}|\sim W$ (2.8 eV, 3.5 eV) for the hole-doped AgAlO$_2$ and AuAlO$_2$, andfinally $T_c$ decreases with increasing $|U_{eff}|$ in the strong couplingregime, where $|U_{eff}| > W$ (1.7 eV), for the hole-doped CuAlO$_2$. In thisstrong coupling regime, one can expect that $T_c$ = 1,000 $\sim$ 2,000 K byassuming the relation of the very strong coupling as $2\Delta / k_{\rm B}T_c$ =50 $\sim$100 and the superconducting gap $\Delta \sim |U_{eff}|$ = 4.53 eV$\sim$ 50,000 K.

Computational materials design of attractive Fermion system with large  negative effective $U$ in the hole-doped Delafossite of CuAlO$_2$, AgAlO$_2$  and AuAlO$_2$