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Multiband Effects on Superconducting Instabilities Driven by Electron-Electron Interactions

We explore multiband effects on d-wave superconducting instabilities driven by electron-electron interactions. Our models on the two-dimensional square lattice consist of a main band with an extended Fermi surface and predominant weight from $d_{x^2-y^2}$ orbitals, whose orbital character is influenced by the admixture of other energetically neighbored orbitals. Using a functional renormalization group description of the superconducting instabilities of the system and different levels of approximations, we study how the energy scale for pairing and hence the critical temperature is affected by the band structure. We find that a reduction of orbital admixture as a function of the orbital energies can cause a $T_c$ enhancement although the Fermi surface becomes more curved and hence less favorable for antiferromagnetic spin fluctuations. While our study does not allow a quantitative understanding of the $T_c$ differences in realistic high-$T_c$ cuprate systems, it may reveal an underlying mechanism contributing to the actual material trends.