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First-principles band structure and FLEX approach to the pressure effect on $T_c$ of the cuprate superconductors

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 contains 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.