The Dominant Role of Critical Valence Fluctuations on High $T_{\rm c}$ Superconductivity in Heavy Fermions

TL;DR

This study reveals that critical valence fluctuations play a dominant role in enhancing superconductivity in heavy fermion compounds, especially near valence crossover points, providing new insights into the pairing mechanism beyond magnetic quantum criticality.

Contribution

It introduces a detailed analysis linking superconducting transition temperature to valence crossover parameters, emphasizing the importance of valence fluctuations in heavy fermion superconductivity.

Findings

Superconducting T_c correlates with valence instability parameter T_cr.

Electrical resistivity near superconductivity is governed by valence crossover.

Optimal T_c is mainly controlled by T_cr and limited by disorder.

Abstract

Despite almost 40 years of research, the origin of heavy-fermion superconductivity is still strongly debated. Especially, the pressure-induced enhancement of superconductivity in CeCu$_2$Si$_2$ away from the magnetic breakdown is not sufficiently taken into consideration. As recently reported in CeCu$_2$Si$_2$ and several related compounds, optimal superconductivity occurs at the pressure of a valence crossover, which arises from a virtual critical end point at negative temperature $T_{\rm cr}$. In this context, we did a meticulous analysis of a vast set of top-quality high-pressure electrical resistivity data of several Ce-based heavy fermion compounds. The key novelty is the salient correlation between the superconducting transition temperature $T_{\rm c}$ and the valence instability parameter $T_{\rm cr}$, which is in line with theory of enhanced valence fluctuations. Moreover, it is found that, in the pressure region of superconductivity, electrical resistivity is governed by the valence crossover, which most often manifests in scaling behavior. We develop the new idea that the optimum superconducting $T_{\rm c}$ of a given sample is mainly controlled by the compound's $T_{\rm cr}$ and limited by non-magnetic disorder. In this regard, the present study provides compelling evidence for the crucial role of critical valence fluctuations in the formation of Cooper pairs in Ce-based heavy fermion superconductors besides the contribution of spin fluctuations near magnetic quantum critical points, and corroborates a plausible superconducting mechanism in strongly correlated electron systems in general.