  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.
