Quantum-Critical, Spin-Fluctuation-driven Residual Resistivity and Emergent Universal Correlations in the Fermi-Liquid Regime of Heavy-Fermion Superconductors

TL;DR

This study reveals universal correlations between residual resistivity, scattering, and superconducting temperature in heavy-fermion superconductors near quantum criticality, emphasizing the role of spin fluctuations in mediating pairing and scattering.

Contribution

It identifies and explains empirical correlations linking spin-fluctuation-driven resistivity, scattering, and superconductivity, and provides a theoretical framework for these phenomena in quantum-critical heavy-fermion systems.

Findings

Empirical correlations between $ ho^{sf}_0$, $A$, and $T_c$ in heavy-fermion superconductors.

Quantum fluctuations mediate both inelastic and elastic scattering channels.

Analytic expressions for $T_c$ and $A$ as functions of a fluctuation-induced length scale.

Abstract

We investigate correlations within the unconventional Fermi-liquid (FL) regime of quantum-critical (QC) heavy-fermion superconductors (HFSs) by tracking the pressure dependence of three quantities: the temperature-independent, SF-driven residual resistivity, $\rho^{ sf}_{0}(P)$; the FL scattering coefficient, $A(P)$; and the superconducting transition temperature, $T_c(P)$. The first two define the spin-fluctuation contribution to the resistivity, $\rho(T)=\rho^{sf}_0+AT^2$. Using experimental data from archetypal heavy-fermion systems, we identify three robust empirical correlations: $\ln(\frac{T_c}{\theta}) \propto A^{-1/2}$, $A \propto (\rho^{sf}_0)^2$, and $\ln(\frac{T_c}{\theta}) \propto \big(\rho^{sf}_0\big)^{-1}$ ($\theta$ is a characteristic temperature scale). Absent in conventional FL superconductors, these relationships indicate that QC fluctuations not only mediate inelastic scattering and Cooper pairing, but also generate an effective elastic channel responsible for $\rho^{sf}_0$. We explicitly calculate $\rho^{sf}_0$ on the high-pressure side of the quantum critical point (QCP) and introduce a characteristic length scale, $\ell \sim \big(\rho^{sf}_0\big)^{-1}$, that captures the spatial extent of fluctuation-induced scattering. Within this regime, and within the Migdal--Eliashberg framework combined with Boltzmann transport theory, we derive analytic expressions for $T_c(\ell)$ and $A(\ell)$, together with their interrelations, which are consistent with the observed empirical trends. These findings highlight the quantum-critical FL regime in HFSs as an intrinsically correlated phase, governed by fluctuations and marked by unconventional transport and pairing mechanisms.