  Extensively reported experimental observations indicate that on varying
pressure ($p$) within the $\textit{T-p}$ phase diagram of most quantum critical
heavy fermion (HF) superconductors, one identifies a cascade of distinct
electronic states which may be magnetic, of Kondo-type, non-conventional
superconducting, Fermi Liquid (FL), or non-FL character. Of particular interest
to this work is the part of the phase diagram lying below a specific phase
boundary, $T^{*}_\text{{FL}}(p^{*})$, across which the transport and
thermodynamic properties switch over from non-FL into FL behavior. Remarkably,
this nontrivial manifestation of FL phase is accompanied by (i) the
characteristic $\rho_o + \textit{AT}^2$ dependence ($\rho_o$ = residual
resistivity), (ii) a superconductivity below $T_{c} \leq
T^{*}_\text{{FL}}(p^{*})$, and (iii) a universal scaling of $T_c$ and $A$:
$ln\frac{T_{c}}{\theta}\propto A^{-\frac{1}{2}}$ ($\theta$ = characteristic
energy scale). We consider that such features are driven by a
fluctuation-mediated electron-electron scattering channel with the mediating
quasiparticles being either spin fluctuations [Mathur et al., Nature 394,39
(1998)] or valence fluctuations [Miyake and Watanabe, Phil. Mag. 97, 3496
(2017)] depending on the character of the neighboring instability. On adopting
such a scattering channel and applying standard theories of Migdal-Eliashberg
(superconductivity) and Boltzmann (transport), we derive analytic expressions
that satisfactorily reproduce the aforementioned empirical correlations in
these heavy fermion superconductors.
