Unconventional superconductivity and an ambient-pressure magnetic quantum critical point in single-crystal ${\mathrm{LaNiC}}_2$

Superconductivity in noncentrosymmetric ${\mathrm{LaNiC}}_2$ is expected to be induced by electron-phonon interactions due to its lack of magnetic instabilities. The non-Bardeen-Cooper-Schrieffer (BCS) behaviors found in this material call into question the long-standing idea that relates unconventional superconductivity with magnetic interactions. Here we report magnetic penetration-depth measurements in a high-purity single crystal of ${\mathrm{LaNiC}}_2$ at pressures up to 2.5 GPa and temperatures down to 0.04 K. At ambient pressure and below $0.5T_c$ the penetration depth goes as $T^4$ for the in-plane and $T^2$ for the out-of-plane component, firmly implying the existence of point nodes in the energy gap and the unconventional character of this superconductor. The present study also provides evidence of magnetism in ${\mathrm{LaNiC}}_2$ by unraveling a pressure-induced antiferromagnetic phase inside the superconducting state at temperatures below 0.5 K, with a quantum critical point around ambient pressure. The results presented here maintain a solid base for the notion that unconventional superconductivity only arises near magnetic order or fluctuations.

Figure 1

Penetration depth shift as a function of temperature in ${\mathrm{LaNiC}}_2$ single crystals at ambient pressure. (a) In-plane ($H\parallel a$ axis) and (b) out-of-plane ($H\perp a$ axis) magnetic penetration depth. $\mathrm{\Delta }{\lambda }_{\text{max}}$ is the total penetration-depth shift from $T_c$ down to the lowest temperature. (b) In-plane and out-of-plane penetration depth in the low-temperature region below $0.5T_c$ (and assuming $T_c=3$ K), from where it is evident that $\mathrm{\Delta }{\lambda }_{\parallel }\propto {(T/T_c)}^4$ and $\mathrm{\Delta }{\lambda }_{\perp }\propto {(T/T_c)}^2$. The inset shows that the digitized specific-heat data of Hirose et al. [21] can also be fitted to a power law $\propto {(T/T_c)}^3$ in the low-temperature limit. Both penetration-depth and heat-capacity measurements in single crystals provide evidence of point nodes in the energy gap of ${\mathrm{LaNiC}}_2$. Lines are guides to the eye.

Figure 2

Superfluid density of ${\mathrm{LaNiC}}_2$ compared with mixed state $A_2$, two-gap, and BCS models in the parallel and perpendicular orientations of the magnetic field with respect to the $a$ axis. We assumed for this graph $T_c=3$ K. The agreement of the experimental data with the state $A_2$ model is outstanding and gives support for the existence of point nodes in the energy gap of ${\mathrm{LaNiC}}_2$.

Figure 3

Penetration depth as a function of temperature and pressure in ${\mathrm{LaNiC}}_2$. (a) In-plane response for various pressures up to 2.48 GPa. With pressure the superconducting transition seems to become sharper and the critical temperature slightly increases. (b) Low-temperature in-plane penetration depth showing sudden upturns followed by abrupt drops at the lowest temperatures. These behaviors are clear indications of the appearance of a pressure-induced magnetic order in ${\mathrm{LaNiC}}_2$. The inset shows for comparison cadmium data taken in the same experimental system.

Figure 4

Phase diagram of ${\mathrm{LaNiC}}_2$, including an antiferromagnetic phase with a quantum critical point inside the superconducting dome.