Correlation between supercondctivity and Fermi-lqiuid transport within the Fermi-liquid regime of quantum-critical heavy-Fermion superconductors

It is remarkable that most reported phase diagrams of quantum critical heavy fermion (HF) superconductors manifest (after being subjected to a higher strength of a control parameter such as pressure) a cascade of distinct electronic states which may be magnetic, of Kondo-type, non-conventional superconducting, Fermi Liquid (FL), or non-FL character[1-3]. It is also remarkable that there is a phase region, the main interst of this work, wherein the superconductivity and normal FL state are neighboring each other and that the normal-state FL quadratic-in-T coefficient ($A$) is correlated with the superconducting transition point ($T_c$). It is usually taken that the surge of these nontrivial features are related to the fluctuation-mediated electron-electron scattering channel with the mediating quasiparticles being either spin fluctuations [4] or valence fluctuations [5] depending on the character of the neighboring instability. Here we consider only the above mentioned FL regime. On adopting such a fluctuation-mediated scattering channel and applying standard theories of Migdal-Eliashberg (superconductivity) and Boltzmann (transport), we derive analytic expressions that reproduce satisfactorily the aforementioned empirical correlations within the above mentioned FL regime..

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