  Pressure effect is overviewed for the cuprates and carbon-based superconductors, with an emphasis on how their orbital characters are modified by pressure. For the high-Tc cuprates, we start from an observation for ambient pressure that, on top of the main orbital (dx2-y2), a hybridization with the second (dz2) orbital around the Fermi energy significantly affects Tc in the spin-fluctuation mediated pairing, where the hybridization is dominated by material parameters. We can then show that applying pressures along a, b axes enhances Tc while a c axis pressure suppresses Tc, where not only the dz2 hybridization but also Cu(4s) hybridization exert an effect. For the multi-layer cuprates, inter-layer pair hopping is suggested to be important, which may contribute to pressure effect. Pressure effect is also interesting in a recently discovered aromatic family of superconductors (picene, etc). There, we have again multi-band systems, which in this case derive from different molecular orbitals. The Fermi surface is an intriguing composite of different pockets/sheets having different dimensionalities arising from anisotropic transfers between the molecular orbitals, and pressure effects should be an important probe of these. 
Pressure effects and orbital characters in cuprate and carbon-based   superconductors