Optical probes of two-component pairing states in transition metal dichalcogenides

Signatures of unconventional superconductivity have been recently observed in certain transition metal dichalcogenides (TMDs), including 4H$_b$-TaS$_2$ and monolayer 2H-NbSe$_2$. While the pairing channel remains unknown, it has been argued that spin fluctuations can stabilize pairing in the two-component $E'$ channel, a $p$-wave spin-triplet state which could be consistent with some of the reported signatures. Exploiting the particular multi-orbital character of the Fermi surface and the presence of Ising spin-orbit coupling, which enable finite optical conductivity in the clean limit, in this work we predict clear-cut optical signatures to detect and distinguish the chiral and nematic ground states of the $E'$ pairing. We quantify how nematic $E'$ states produce a diagonal anisotropy $\sigma_{xx}\!\neq\!\sigma_{yy}$ due to the broken threefold symmetry ($C_3$), while chiral $E'$ states yield a finite optical Hall conductivity $\sigma_{xy}^H$ due to broken time-reversal symmetry, and find both signals could be detected in current experiments. For instance, for realistic gaps in the meV range, we predict a relative anisotropy $\Delta\sigma/\sigma\sim10^{-5}$ in the nematic states, and a polar Kerr rotation of $\theta_K\!\sim\!10^{-5}$ rad in the chiral states. These symmetry fingerprints provide a practical route to distinguish nematic and chiral superconducting order in TMD superconductors.