Anisotropic multiband superconductivity in $2M\text{−}{\text{WS}}_2$ probed by controlled disorder

The intrinsically superconducting Dirac semimetal $2M\text{−}{\mathrm{WS}}_2$ is a promising candidate for realizing proximity-induced topological superconductivity in its protected surface states. A precise characterization of the bulk superconducting state is essential to understand the nature of surface superconductivity in the system. Here, we report a detailed experimental study of the temperature-dependent London penetration depth, $\lambda \left(T\right)$, the upper critical field, $H_{c2}\left(T\right)$, and the effects of nonmagnetic disorder on these quantities, as well as on the superconducting transition temperature $T_c$ in single crystals of $2M\text{−}{\mathrm{WS}}_2$. We observe a power-law variation of $\lambda \left(T\right)\propto T^3$ at temperatures below $0.35T_c$. Nonmagnetic pointlike disorder induced by 2.5 MeV electron irradiation at various doses results in a significant suppression of $T_c$. These observations are markedly different from expectations for a fully gapped isotropic $s\text{−}\mathrm{wave}$ superconductor. Together with the substantial increase of slope, $d{H}_{c2}{/dT|}_{T=T_c}$, with increasing disorder, our results suggest a strongly anisotropic $s^{++}$ multiband superconducting state. These results have direct consequences for the expected proximity-induced superconductivity of the topological surface states.