Second and third harmonic generation in topological insulator-based van der Waals metamaterials

High-order harmonic generation (HHG) in solids-the frequency up-conversion of an optical signal-is governed by symmetries. At terahertz (THz) frequencies, HHG is a key technology to access high-frequency spectral windows that are usually difficult to cover using conventional solid-state laser technologies. This effect has been recently exploited in graphene, where HHG has been demonstrated, albeit only at odd multiples of the driving frequency owing to its inherent centro-symmetry. In topological insulators (TIs), the combination of spin-orbit interaction and time-reversal symmetry create an insulating bulk state with an inverted band order, inseparably connected with conducting surface states. TIs have been predicted to support unconventional high harmonic generation from the bulk and topological surface, which are usually difficult to distinguish. However, no experimental results have been reported, so far. Here, we exploit the strong optical field amplification provided by an array of single or double split ring resonators, with embedded Bi₂Se₃ or (In_xBi_(1-x))₂Se₃/Bi₂Se₃ Van der Waals heterostructures, to achieve up-conversion in the 6.4 (even)-9.7 (odd) THz frequency range. This results from bulk centro-symmetry (odd states) and symmetry breaking in the topological surface states (odd and even).