Topological Ising pairing states in monolayer and trilayer TaS2

We study the possibility of topological superconductivity in the noncentrosymmetric monolayer and trilayer ${\mathrm{TaS}}₂$ with out-of-plane mirror symmetry. A time-reversal-invariant nodal $(s+f)$-wave pairing state with even mirror parity is found to be a promising candidate. This mixed state holds 12 (36) nodes at the Fermi pockets around $\mathrm{\ensuremath{\Gamma}}$ for the monolayer (trilayer) case and its unconventional superconductivity is consistent with the scanning tunneling microscopy experiments observed in $2H\text{\ensuremath{-}}{\mathrm{TaS}}₂$ thin flakes. Furthermore, with doping or under uniaxial pressure for trilayer $2H\text{\ensuremath{-}}{\mathrm{TaS}}₂$, large-Chern-number time-reversal symmetry-breaking mixed states between $(d+id)$- and $(p\ensuremath{-}ip)$-wave pairings can be realized in the phase diagram.