Considerations on the mechanisms and transition temperatures of superconductivity induced by electronic fluctuations.

An overview of the momentum and frequency dependence of effective electron-electron interactions which favor electronic instability to a superconducting state in the angular-momentum channel ℓ and the properties of the interactions which determine the magnitude of the temperature T(c) of the instability is provided. Interactions induced through exchange of electronic fluctuations of spin density, charge density or current density are considered. Special attention is paid to the role of quantum-critical fluctuations (QCFs) including pairing due to their virtual exchange as well as de-pairing due to inelastic scattering. Additional insight is gained by reviewing empirical data and theory specific to superfluidity in liquid He(3), superconductivity in some of the heavy-fermion compounds, in cuprates, in pncitides and the valence skipping compound. The physical basis for the following observation is provided: the ratio of the maximum T(c) to the typical phonon frequency in phonon induced s-wave superconductivity is O(10(-1)); the ratio of p-wave T(c) to the renormalized Fermi energy in liquid He(3), a very strongly correlated Fermi liquid near its melting pressure, is only O(10(-3)); in the cuprates and the heavy fermions where d-wave superconductivity occurs in a region governed by QCFs, this ratio rises to O(10(-2)). These discussions also suggest factors important for obtaining higher T(c). Experiments and theoretical investigations are suggested to clarify the many unresolved issues.