Nodeless superconductivity and topological nodal states in molybdenum carbide

The orthorhombic molybdenum carbide superconductor with $T_c$ = 3.2 K was investigated by muon-spin rotation and relaxation ($\mu$SR) measurements and by first-principle calculations. The low-temperature superfluid density, determined by transverse-field $\mu$SR, suggests a fully-gapped superconducting state in Mo$_2$C, with a zero-temperature gap $\Delta_0$ = 0.44 meV and a magnetic penetration depth $\lambda_0$ = 291 nm. The time-reversal symmetry is preserved in the superconducting state, as confirmed by the absence of an additional muon-spin relaxation in the zero-field $\mu$SR spectra. Band-structure calculations indicate that the density of states at the Fermi level is dominated by the Mo $4d$-orbitals, which are marginally hybridized with the C $2p$-orbitals over a wide energy range. The symmetry analysis confirms that, in the absence of spin-orbit coupling (SOC), Mo$_2$C hosts twofold-degenerate nodal surfaces and fourfold-degenerate nodal lines. When considering SOC, the fourfold-degenerate nodal lines cross the Fermi level and contribute to the electronic properties. Our results suggest that, similarly to other phases of carbides, also the orthorhombic transition-metal carbides host topological nodal states and may be potential candidates for future studies of topological superconductivity.