Nematic superconductivity in the topological semimetal CaSn$_{3}$

The superconducting behavior of the topological semimetal CaSn$_{3}$ was investigated by means of magnetotransport and muon spectroscopy $\mu$SR measurements, both providing strong evidence of nematic behavior. Magnetotransport detects an anisotropic upper critical field, characterized by a twofold symmetry about $C_{4}$ axis, thus breaking the rotational symmetry of the underlying cubic lattice. Transverse-field $\mu$SR data support such picture, with the muon depolarization rate depending strongly on the magnetic field direction, here applied along the [110] or [001] crystal directions. In the former case, the absence of any additional muon depolarization suggests an unconventional vortex lattice. In the latter case, a vortex lattice encompassing a sample volume of at least 52% indicates the bulk nature of CaSn$_{3}$ superconductivity. The resulting superfluid density in the (001) planes shows a gapped low-temperature behavior, with a superconducting gap value $\Delta(0)\simeq 0.61(7)$ meV. Additional zero-field $\mu$SR results indicate that the superconducting state is time-reversal-invariant. This fact and the breaking of rotational symmetry in a fully-gapped superconductor are consistent with an unconventional pairing state in a multi-dimensional representation, thus making CaSn$_{3}$ an important example of nematic superconductor.