  To show an optimization method of element substitution for cuprate
superconductors, we investigate Fermi surface shape of TlR2A2Cu3O9 with R=La,
Y, and A=Li, Na, K, Rb, Cs. We adopt the generalized gradient approximation in
the density-functional theory (DFT-GGA) for the study of over-doped phases of
these unknown cuprates. The electronic structures of crystals optimized by
DFT-GGA show systematic element dependence in a Fermi surface shape controlling
parameter, r, of Cu dx2-y2 bands, where nearly absent dz2 component at the
Fermi level and smaller r keeping t1 suggest enhancement of the superconducting
transition temperature within the spin-fluctuation mechanism. For TlYRb2Cu3O9,
smaller r by a reduction factor larger than 10% compared to a reference system
of TlBa2Ca2Cu3O9 (TBCCO) appears in the outer CuO2 plane, but with 12 %
reduction in t1. For TlR2Li2Cu3O9, (R=Y, La), smaller r by a factor larger than
1% appears keeping t1 as large as TBCCO in the inner plane. Our method may be
used to predict an optimized material structure referencing known cuprate
superconductors.
