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Abstract: An overview of the momentum and frequency dependence of effectiveelectron-electron interactions which favor electronic instability to asuperconducting state in the angular-momentum channel $\ell$ and the propertiesof the interactions which determine $T c$ is provided. Both interactionsinduced through exchange of phonons as well as purely electronic fluctuationsof spin density, charge density or current density are considered. Specialattention is paid to the role of quantum critical fluctuations includingpairing due to their virtual exchange as well as de-pairing due to inelasticscattering. In light of the above, empirical data and theory specific to phononinduced superconductivity, in cold atoms, superfluidity in liquid $He^3$,superconductivity in some of the heavy fermion compounds, in Cuprates, inpncitides and the valence skipping compound, is reviewed. The physical basisfor the following observation is provided: The universal ratio of s-wave $T c$to Fermi-energy for fermions at the unitarity limit with attractiveinteractions is about 0.15, the ratio of the maximum $T c$ to the typicalphonon frequency in phonon induced s-wave superconductivity is of the sameorder; 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, isonly $O10^{-3}$; in the Cuprates and the heavy-fermions where d-wavesuperconductivity occurs in a region governed by a special class ofquantum-critical fluctuations, this ratio rises to $O10^{-2}$. Thesediscussions also suggest factors important for obtaining higher $T c$.



Author: C.M. Varma

Source: https://arxiv.org/







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