Nonlinear Optical Responses in Multi-Orbital Topological Superconductors

We study the non-linear optical responses of a multi-band noncentrosymmetric superconductor. The absence of inversion symmetry in noncentrosymmetric superconductors allows for the coexistence of opposite parity pairing channels, thus leading to a mixed-parity order parameter with mixed-parity pairing terms. These factors can give rise to exotic properties, including topological superconductivity. The nature of the superconducting phase is determined by the intricate interplay of Rashba spin-orbit coupling and the inter- and intra-orbital pairing amplitudes. These aspects of the system can be utilized to drive a phase transition from trivial to topological superconducting phases. We explore the suitability of the second-order conductivity as a probe for studying the topological nature of the superconducting phase of the system. We find that the second-order response, in contrast with the linear response, contains clear signatures that can be used to differentiate between trivial and topological superconducting phases. In particular, the low-frequency second-order DC response, also known as the photogalvanic response, exhibits distinctive features in different phases, indicating that it can serve as a potential probe to determine the topological nature of the superconducting state.