One pressure range, three directions
The central finding is a shared transport pattern. As pressure approached the range where superconductivity emerged, CeNiC2 showed the same evolution in electrical resistivity whether current ran along its a, b or c axis. The fitted residual resistivity, the part left after the temperature-dependent contribution is modeled, reached a pronounced maximum near 9.5 to 10 GPa for all three directions. The temperature exponent n followed the same pressure trend on each axis and approached 1, indicating an almost linear change in resistivity with temperature. This is the feature the authors interpret as nearly isotropic critical scattering, meaning the critical transport signal looked similar despite the crystal's different directions.
That comparison was the study's central test. The researchers asked whether the T-linear resistivity seen near the pressure-induced superconducting dome was confined to one crystallographic direction or common to all three. Their measurements favored the common-pattern reading within this material and pressure range. The authors interpret simultaneous T-linear transport and the enhancement of fitted residual resistivity as support for a valence-fluctuation explanation of the nearly isotropic scattering. The work does not directly measure valence fluctuations, so the proposed mechanism remains an interpretation of the transport behavior.
How the comparison was made
To make the comparison, the researchers grew CeNiC2 single crystals and checked their phase purity and orientation with single-crystal x-ray diffraction. They then used four-probe resistivity measurements with current separately aligned along the a, b and c axes under pressure. Zero-field measurements covered 2 to 300 K, reaching pressures up to 13 GPa for current along a and 12 GPa for current along b and c. For selected measurements with current along b, the field study reached 20 mK and 9 T at pressures of about 10.4 to 10.5 GPa.
For the transport analysis, the data were averaged in 0.5-K intervals. The researchers fitted resistivity to the form rho(T) = rho0 + A T^n, beginning 5 K above the superconducting transition and excluding magnetic-transition regions. They also checked n with a logarithmic derivative, a separate way of testing how the temperature-dependent part changes. The comparison therefore followed both the fitted residual term and the temperature exponent as pressure changed.
At ambient pressure, the single crystals still showed ordinary directional differences. Resistivity was highest with current along b, followed by c and a. The reported residual-resistivity ratios were approximately 23, 50 and 39 for a, b and c, respectively. Residual resistivities were 2.46, 5.02 and 4.42 micro-ohm centimetres along those axes, all below the 9.85 micro-ohm centimetres reported for a polycrystalline specimen. The comparison began with lower residual resistivity in the single crystals than in the reported polycrystal, even though the three axes differed.
A narrow superconducting window
Superconductivity appeared near 9 GPa and formed a narrow dome. Its resistive onset reached about 3.8 K for current along a near 9.7 GPa, about 3.84 K along b near 9.6 GPa, and about 3.9 K along c near 9.5 GPa. Zero resistance extended to 10 GPa in the a-axis run and roughly 10.4 GPa in the b-axis run. Those onset temperatures sit in the same pressure neighborhood as the common maximum in fitted residual resistivity and the approach of n to 1.
The report's magnetic-transition temperature, TICAF, rose from about 19 K to near 34 K at approximately 7 GPa, then decreased until it became unresolved near 10 GPa. A Kondo/coherence scale, TK, appeared between 4 and 6 GPa and shifted rapidly to higher temperature above about 8 GPa. These results show that magnetic and Kondo-related scales were changing as the transport anomaly developed, but the resistivity measurements alone do not directly distinguish the proposed valence picture from those accompanying pressure-dependent changes.
In field tests with current along b, fields up to 9 T shifted the superconducting transition to lower temperature while leaving the normal-state T-linear resistivity nearly unchanged. At about 10.4 GPa for field along a and 10.5 GPa for field along c, the extrapolated upper critical fields were approximately 19.8 T and 15.0 T, respectively. Their ratio was about 1.3, and both exceeded the weak-coupling Pauli field. The result adds a moderate field-direction difference to a study whose normal-state critical transport was otherwise common across the three current directions.
A proposed mechanism still needs a direct test
The evidence also has practical limits. The three current directions were measured in independent pressure runs and compared using nearest pressure points, not always identical pressures. Formal uncertainty estimates and confidence intervals were not reported, and the maximum pressure differed between the runs, reaching 13 GPa for a versus 12 GPa for b and c. Superconductivity was assessed through resistive onset and zero-resistance criteria; thermodynamic confirmation was not reported. A direct test of the authors' valence picture would require pressure-dependent Ce L-edge x-ray absorption or resonant x-ray spectroscopy, along with independent microscopic probes.
Paper data and sources
Original title: Nearly Isotropic Quantum-Critical Transport in Single-Crystal CeNiC2
Authors: Hanming Ma, Jun Gouchi, Dilip Bhoi et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
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