Electronic structures and transition temperatures of high-Tc cuprate superconductors from first-principles calculations and Landau theory

First-principles calculations are employed to investigate atomic and electronic structures and superconductivity properties of (Tl, Pb)(Ba, Sr)2Can−1CunO2n+3 [(Tl, Pb)(Ba, Sr)-12(n-1)n], HgBa2Can−1CunO2n+2+δ [Hg-12(n-1)n] (n = 1, 2, 3, 4), and La2−xSrxCuO4 (LSCO) high-Tc cuprate superconductors. The calculated geometric structures agree well with the experimental data. The electronic structures of (Tl, Pb)(Ba, Sr)-12(n-1)n, Hg-12(n-1)n, and LSCO cuprate superconductors show flat bands (FB) near the Fermi levels, a feature favorable for superconductivity. Based on the electronic structure calculations and Landau theory, we propose that the total length of the FB segments (∑iLiFB=∑i|k→iFB|) determines the superconducting transition temperature (Tc) of (Tl, Pb)(Ba, Sr)-12(n-1)n, Hg-12(n-1)n, and LSCO systems – a greater length corresponds to a higher Tc, i.e., Tc∼∑iLiFB. This finding is consistent with the recent experimental observation that Tc scales with the zero temperature phase stiffness (the superfluid density), which points to local pairs (i.e. FB) rather than conventional BCS physics. This work could be helpful for designing and finding new unconventional superconductors.