Crystal growth, characterization and advanced study of the noncentrosymmetric superconductor Mo$_3$Al$_2$C

We report on the first successful growth of single crystals of the noncentrosymmetric superconductor Mo$_3$Al$_2$C obtained by means of a cubic-anvil, high-pressure and high-temperature technique. Composition, structure, and normal-state transport properties of the crystals were studied by means of X-ray diffraction, energy-dispersive X-ray spectroscopy, magnetic susceptibility and resistivity measurements as a function of temperature. Variations in critical temperature ($T_c$) between 8.6 and 9.3 K were observed, probably due to the slightly different carbon stoichiometry of the samples. Single-crystal X-ray refinement confirmed the high structural perfection of the grown crystals. Remarkably, the refined Flack parameter values for all the measured crystals using a $P4_132$ space-group model were consistently close to either 0 or 1, hence indicating that the considered crystals belong to two enantiomorphic space groups, $P4_132$ and $P4_332$. An anomaly in the resistivity is observed at about 130 K, most likely associated with the onset of a charge-density-wave phase. The superconducting properties (and in particular the symmetry, the amplitude and the temperature dependence of the superconducting gap) were studied by using - for the first time in this compound - point contact Andreev-reflection spectroscopy. The results confirm that Mo$_3$Al$_2$C is a moderately strongly-coupled superconductor with $2\Delta/k_BT_c \simeq 4$ and unambiguously prove that the order parameter has an s-wave symmetry despite the asymmetric spin-orbit coupling arising from the lack of inversion symmetry.