Two-Particle Self-Consistent Analysis for the Electron-Hole Asymmetry of Superconducting Transition Temperature in High-$T_{c}$ Cuprates

The striking electron-hole doping asymmetry in the doping dependence of $T_{c}$ is among unsolved issues in the study of the high-$T_{c}$ cuprate superconductors. It is well-known that in the hole-doped case, $T_{\mathrm{c\thinspace }}$exhibits a dome-like feature against the doping rate. On the other hand, $T_{\mathrm{c\thinspace }}$in the electron-doped systems monotonically increases as the doping is reduced, at least down to a very small doping rate$^{\mathrm{\thinspace [1,2]}}$. To understand the origin of this electron-hole asymmetry of $T_{\mathrm{c}}$, we perform the Two-Particle Self-Consistent (TPSC) analysis$^{\mathrm{\thinspace [3]}}$ for the three-band $d-p$ model constructed from the first principles calculation $^{\mathrm{[4]}}$. The obtained doping dependence reproduces the asymmetric behavior of $T_{\mathrm{c}}$. This is explained as a combined effect of the intrinsic electron-hole asymmetry in systems comprising Cu3$d$ and O2$p$ orbitals and the band-filling-dependent vertex correction. References: [1] M. Brinkmann, et al., Phys. Rev. Lett. \textbf{74}, 4927 (1995). [2] A. Tsukada, et al., Solid State Commun. \textbf{133},427 (2005). [3] Y. Vilk and A.-M. Tremblay, J. Phys. I (France) \textbf{7}, 1309 (1997). [4] A. A. Mostofi, et al., Phys. Commun.\textbf{ 178}, 685 (2008).