Nonlinear optical responses in multi-orbital topological superconductors

We theoretically study first and second-order optical responses in a transition metal dichalcogenide monolayer with distinct trivial, nodal, and time-reversal invariant topological superconducting (TRITOPS) phases. We show that the second-order DC response, also known as the photogalvanic response, contains signatures for differentiating these phases while the first-order optical response does not. We find that the high-frequency photogalvanic response is insensitive to the phase of the system, while the low-frequency response exhibits features distinguishing the three phases. At zero doping, corresponding to an electron filling in which the Fermi level lies at nodal points, there are opposite sign zero-frequency divergences in the response when approaching the nodal phase boundaries from the trivial and the TRITOPS phases. In the trivial phase, both the high-frequency and low-frequency response of the system are negative, but in the TRITOPS phase, the low-frequency response becomes positive while the high-frequency response remains negative. Furthermore, since phase transitions are controlled by the Rashba spin-orbit coupling and the ratio of intra-orbital and inter-orbital paring amplitudes, our results not only help distinguish the phases but can also provide an estimate of the pairing amplitudes based on the photogalvanic response of the system.