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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 compounds $T_{rm cr}$ 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.
We report the novel pressure(P)-temperature(T) phase diagrams of antiferromagnetism (AF) and superconductivity (SC) in CeRhIn$_5$, CeIn$_3$ and CeCu$_2$Si$_2$ revealed by the NQR measurement. In the itinerant helical magnet CeRhIn$_5$, we found that
Motivated by the widespread experimental observations of nematicity in strongly underdoped cuprate superconductors, we investigate the possibility of enhanced nematic fluctuations in the vicinity of a Mott insulator that displays Neel-type antiferrom
In solids containing elements with f orbitals, the interaction between f-electron spins and those of itinerant electrons leads to the development of low-energy fermionic excitations with a heavy effective mass. These excitations are fundamental to th
A $^{59}$Co nuclear quadrupole resonance (NQR) was performed on a single-crystalline ferromagnetic (FM) superconductor UCoGe under pressure. The FM phase vanished at a critical pressure $P_c$, and the NQR spectrum just below $P_c$ showed phase separa
Understanding the complexities of electronic and magnetic ground states in solids is one of the main goals of solid-state physics. Materials with the canonical ThCr$_2$Si$_2$-type structure have proved particularly fruitful in this regards, as they e