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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 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., Comment: Supplementary Material follows after the bibliography

We present the pressure-temperature phase diagram of the antiferromagnet CeAg$_2$Si$_2$ established via resistivity and calorimetry measurements under quasi-hydrostatic conditions up to 22.5~GPa. With increasing pressure, the N\'eel temperature [$T_{\mathrm{N}}(p=0)=8.6$~K] slowly increases up to $T_{\mathrm{N}}=13.4$~K at 9.4~GPa and then vanishes abruptly at the magnetic critical pressure $p_{\mathrm{c}}\sim13$~GPa. For the first time, heavy fermion superconductivity is observed in CeAg$_2$Si$_2$ . Superconductivity emerges at $\sim 11$~GPa and persists over roughly 10~GPa. Partial- and bulk-transition temperatures are highest at $p=16$~GPa, with a maximal $T_{\mathrm{c}^{\rm bulk}}=1.25$~K. In the pressure region of superconductivity, Kondo and crystal-field splitting energies become comparable and resistivity exhibits clear signatures of a Ce-ion valence crossover. The crossover line is located at a rapid collapse in resistivity as function of pressure and extrapolates to a valence transition critical endpoint at critical pressure and temperature of $p_{\rm cr}\sim 17$~GPa and $T_{\rm cr}\sim-13~K$, respectively. Both critical spin and valence fluctuations may build up superconductivity in CeAg$_2$Si$_2$.

The pressure-temperature-phase diagram of the new heavy-fermion superconductor CeAu$_2$Si$_2$ is markedly different from those studied previously. Indeed, superconductivity emerges, not on the verge, but deep inside the magnetic phase. In this context, we have carried out ac-calorimetry, resistivity and thermoelectric power measurements on a CeAu$_2$Si$_2$-single crystal under high-pressure. The principal novelties of this experiment are the observation of a new transition line, presumably a magnetic structure rearrangement at $T_{\mathrm{M}}^{\mathrm{mod}}$ inside the antiferromagnetic phase, and the occurrence of quantum critical behavior in resistivity linked to superconductivity. Strong non-Fermi-liquid behavior is observed around the maximum of superconductivity and enhanced scattering rates are observed close to both the emergence and the maximum of superconductivity. Intriguingly, $T_{\mathrm{M}}^{\mathrm{mod}}$ almost coincides with the onset of the superconducting transition over a broad pressure range, where mysteriously Tc increases with the strengthening of magnetism. A comparison of the features in CeAu$_2$Si$_2$ and its parent compounds CeCu$_2$Si$_2$ and CeCu$_2$Ge$_2$ plotted as function of the unit-cell volume leads us to promote that critical fluctuations of a valence crossover play a crucial role in the superconducting paring mechanism. Our study reveals new intriguing features of magnetism and illustrates a complex interplay between magnetism, quantum criticality and superconductivity., Comment: 10 pages, 10 figures

We present measurements of the magnetoresistivity RHOxx of URu2Si2 single crystals in high magnetic fields up to 60 T and at temperatures from 1.4 K to 40 K. Different orientations of the magnetic field have been investigated permitting to follow the dependence on Q of all magnetic phase transitions and crossovers, where Q is the angle between the magnetic field and the easy-axis c. We find out that all magnetic transitions and crossovers follow a simple 1/cos(Q) -law, indicating that they are controlled by the projection of the field on the c-axis.