Our recent study has revealed that the mixture of the dz2 orbital component into the Fermi surface suppresses Tc in the cuprates such as La2CuO4. We have also shown that applying hydrostatic pressure enhances Tc due to smaller mixing of the Cu4s comp
onent. We call these the orbital distillation effect. In our previous study, the 4s orbital was taken into account through the hoppings in the dx2-y2 sector, but here we consider a model in which of the dx2-y2, dz2 and 4s orbitals are all considered explicitly. The present study reinforces our conclusion that smaller 4s hybridization further enhances Tc.
High-temperature cuprate superconductors have been known to exhibit significant pressure effects. In order to fathom the origin of why and how Tc is affected by pressure, we have recently studied the pressure effects on Tc adoptig a model that contai
ns two cupper d-orbitals derived from first-principles band calculations, where the dz2 orbital is considere on top of the usually considered dx2-y2 orbital. In that paper, we have identified two origins for the Tc enhancement under hydrostatic pressure: (i) while at ambient pressure the smaller the hybridization of other orbital components the higher the Tc, an application of pressure acts to reduce the multiorbital mxing on the Fermi surface, which we call the orbital distillation effects, and (ii) the increase of the band width with pressure also contributes to the enhancement. In the present paper, we further elabolrate the two points. As for point (i), while the reduction of the apical oxygen height under pressure tends to increase the dz2 mixture, hence to lower Tc, here we show that this effect is strongly reduced in bi-layer materials due to the pyramidal coordination of oxygen atoms. As for point (ii), we show that the enhancement of Tc due to the increase in the band width is caused by the effect that the many-body renormalization arising from the self-energy is reduced.
The origin of uniaxial and hydrostatic pressure effects on $T_c$ in the single-layered cuprate superconductors is theoretically explored. A two-orbital model, derived from first principles and analyzed with the fluctuation exchange approximation give
s axial-dependent pressure coefficients, $partial T_c/partial P_a>0$, $partial T_c/partial P_c<0$, with a hydrostatic response $partial T_c/partial P>0$ for both La214 and Hg1201 cuprates, in qualitative agreement with experiments. Physically, this is shown to come from a unified picture in which higher $T_c$ is achieved with an orbital distillation, namely, the less the $d_{x^2-y^2}$ main band is hybridized with the $d_{z^2}$ and $4s$ orbitals higher the $T_c$. Some implications for obtaining higher $T_c$ materials are discussed.
In order to understand the material dependence of $T_c$ within the single-layered cuprates, we study a two-orbital model that considers both $d_{x^2-y^2}$ and $d_{z^2}$ orbitals. We reveal that a hybridization of $d_{z^2}$ on the Fermi surface substa
ntially affects $T_c$ in the cuprates, where the energy difference $Delta E$ between the $d_{x^2-y2}$ and $d_{z^2}$ orbitals is identified to be the key parameter that governs both the hybridization and the shape of the Fermi surface. A smaller $Delta E$ tends to suppress $T_c$ through a larger hybridization, whose effect supersedes the effect of diamond-shaped (better-nested) Fermi surface. The mechanism of the suppression of d-wave superconductivity due to $d_{z^2}$ orbital mixture is clarified from the viewpoint of the ingredients involved in the Eliashberg equation, i.e., the Greens functions and the form of the pairing interaction described in the orbital representation. The conclusion remains qualitatively the same if we take a three-orbital model that incorporates Cu 4s orbital explicitly, where the 4s orbital is shown to have an important effect of making the Fermi surface rounded. We have then identified the origin of the material and lattice-structure dependence of $Delta E$, which is shown to be determined by the energy difference $Delta E_d$ between the two Cu3d orbitals (primarily governed by the apical oxygen height), and the energy difference $Delta E_p$ between the in-plane and apical oxygens (primarily governed by the interlayer separation $d$).
In order to explore the reason why the single-layered cuprates, La$_{2-x}$(Sr/Ba)$_x$CuO$_4$ ($T_csimeq$ 40K) and HgBa$_2$CuO$_{4+delta}$ ($T_csimeq$ 90K), have such a significant difference in $T_c$, we study a two-orbital model that incorporates th
e $d_{z^2}$ orbital on top of the $d_{x^2-y^2}$ orbital. It is found, with the fluctuation exchange approximation, that the $d_{z^2}$ orbital contribution to the Fermi surface, which is stronger in the La system, works against d-wave superconductivity, thereby dominating over the effect of the Fermi surface shape. The result resolves the long-standing contradiction between the theoretical results on Hubbard-type models and the experimental material dependence of $T_c$ in the cuprates.
