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 $(\ensuremath{\mu}\mathrm{SR})$ measurements and by first-principles calculations. The low-temperature superfluid density, determined by transverse-field $\ensuremath{\mu}\mathrm{SR}$, suggests a fully gapped superconducting state in ${\mathrm{Mo}}_{2}\mathrm{C}$, with a zero-temperature gap ${\mathrm{\ensuremath{\Delta}}}_{0}=0.44$ meV and a magnetic penetration depth ${\ensuremath{\lambda}}_{0}=291$ 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 $\ensuremath{\mu}\mathrm{SR}$ spectra. Band-structure calculations indicate that the density of states at the Fermi level is dominated by the $\mathrm{Mo}\text{\ensuremath{-}}4d$ orbitals, which are marginally hybridized with the $\mathrm{C}\text{\ensuremath{-}}2p$ orbitals over a wide energy range. The symmetry analysis confirms that, in the absence of spin-orbit coupling (SOC), ${\mathrm{Mo}}_{2}\mathrm{C}$ 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.