Circuit quantum electrodynamics simulator of the two-dimensional Su-Schrieffer-Heeger model: higher-order topological...

Higher-order topological insulator (HOTI) occupies an important position in topological band theory due to its exotic bulk-edge correspondence. Recently, it has been predicted that external magnetic field can induce novel topological phases in 2D HOTIs. However, up to now the theoretical description is still incomplete and the experimental realization is still lacking. Here we proposed a superconducting quantum circuit simulator of 2D Su-Schriffer-Heeger lattice, which is one of the most celebrated HOTI models, and investigate consequently the influence of the continuously varying magnetic field. By using the parametric conversion coupling method, we can establish in principle the time- and site-resolved tunable hopping constants in the proposed architecture, thus providing an ideal platform for investigating the higher-order topological phase transitions induced by continuously varying magnetic field. Our numerical calculation further shows that the higher-order topology of the lattice, which manifests itself through the existence of the zero energy corner modes, exhibit exotic and rich dependence on the imposed magnetic field and the inhomogeneous hopping strength. To probe the proposed magnetic-field-induced topological phase transition, we study the response of the lattice to the corner site pumping in the steady state limit, with results implying that the predicted topological phase boundaries can be unambiguously identified by the measurement of the corner sites and their few neighbors. Requiring only current level of technology, our scheme can be readily tested in experiment and may pave an alternative way towards the future investigation of HOTIs under various mechanisms including magnetic field, disorder, and strong correlation.