Unlocking nonlinear optical phenomena due to spin-orbit and Zeeman interactions in the graphene family topological insulators

Two-dimensional buckled monolayers of the graphene family, namely silicene, germanene, stanene, and plumbene, possess non-negligible intrinsic spin-orbit coupling which opens a gap in the Dirac-like energy band structure. Each gap can be tailored with external fields to drive the system via different topologically insulating phases. Due to the in-plane spatial symmetry of the low energy Hamiltonian of these materials, investigations of their nonlinear optical response within the electric dipole approximation have been limited to odd-order harmonics. In this work, we show that although a Rashba spin-orbit coupling and an in-plane Zeeman interaction cannot independently break this in-plane spatial symmetry, together they are able to do so, which leads to a nonlinear optical response that includes the generation of even harmonics. We further explore the effect of second harmonic generation near various topological phase transitions.