Double resonance between corner states in distinct higher-order topological phases

Recent studies have shown that higher-order topologies in photonic systems lead to a robust enhancement of light-matter interactions. Moreover, higher-order topological phases have been extended to systems even without a band gap, as in Dirac semimetals. In this work, we propose a procedure to simultaneously generate two distinctive higher-order topological phases with corner states that allow a double resonant effect. This double resonance effect between the higher-order topological phases, was obtained from the design of a photonic structure with the ability to generate a higher-order topological (HOTI) insulator phase in the first bands and a higher-order Dirac half-metal phase (HODSM). Subsequently, using the corner states in both topological phases, we tuned the frequencies of both corner states such that they were separated in frequency by a second harmonic. This idea allowed us to obtain a double resonance effect with ultra-high overlap factors, and a considerable improvement in the nonlinear conversion efficiency. These results show the possibility of producing a second-harmonic generation with unprecedented conversion efficiencies in topological systems with simultaneous HOTI and HODSM phases. Furthermore, since the corner state in the HODSM phase presents an algebraic 1/rdecay, our topological system can be helpful in experiments about the generation of nonlinear Dirac-ligh-matter interactions.