Evidence for charge delocalization crossover in the quantum critical superconductor CeRhIn$_5$

The nature of charge degrees-of-freedom distinguishes scenarios for interpreting the character of a second order magnetic transition at zero temperature, that is, a magnetic quantum critical point (QCP). Heavy-fermion systems are prototypes of this paradigm, and in those, the relevant question is where, relative to a magnetic QCP, does the Kondo effect delocalize their $f$-electron degrees-of-freedom. Herein, we use pressure-dependent Hall measurements to identify a finite-temperature scale $E_\text{loc}$ that signals a crossover from $f$-localized to $f$-delocalized character. As a function of pressure, $E_\text{loc}(P)$ extrapolates smoothly to zero temperature at the antiferromagnetic QCP of CeRhIn$_5$ where its Fermi surface reconstructs, hallmarks of Kondo-breakdown criticality that generates critical magnetic and charge fluctuations. In 4.4% Sn-doped CeRhIn$_5$, however, $E_\text{loc}(P)$ extrapolates into its magnetically ordered phase and is decoupled from the pressure-induced magnetic QCP, which implies a spin-density-wave (SDW) type of criticality that produces only critical fluctuations of the SDW order parameter. Our results demonstrate the importance of experimentally determining $E_\text{loc}$ to characterize quantum criticality and the associated consequences for understanding the pairing mechanism of superconductivity that reaches a maximum $T_\text{c}$ in both materials at their respective magnetic QCP.