Nonlinear quadrupole topological insulators

Higher-order topological insulators (HOTIs) represent a family of topological phases that go beyond the conventional bulkboundary correspondence. d-dimensional n-th order HOTIs maintain (d - n)-dimensional gapless boundary states (in particular, zero-dimensional corner states in the case of d = n = 2). HOTIs of the Wannier type cam be extended into the nonlinear regime. Another prominent class of HOTIs, in the form of multipole insulators, was investigated only in the linear regime, due to the challenge of simultaneously achieving both negative hopping and strong nonlinearity. Here we propose the concept of nonlinear quadrupole topological insulators (NLQTIs) and report their experimental realization in an electric circuit lattice. Quench-initiated dynamics gives rise to nonlinear topological corner states and topologically trivial corner solitons, in weakly and strongly nonlinear regimes, respectively. Furthermore, we reveal the formation of two distinct types of bulk solitons, one existing in the middle finite gap under the action of weak nonlinearity, and another one found in the semi-infinite gap under strong nonlinearity. This work realizes another member of the nonlinear HOTI family, suggesting directions for exploring novel solitons across a broad range of topological insulators.

💡 Research Summary

The authors introduce and experimentally realize a nonlinear quadrupole topological insulator (NLQTI), extending the concept of higher‑order topological insulators (HOTIs) into the nonlinear regime. In conventional quadrupole topological insulators (QTIs) the quantized quadrupole moment q_xy = ½ protects zero‑dimensional corner states, but achieving both negative hopping and strong nonlinearity has been a major obstacle. To overcome this, the team designs an electric‑circuit lattice in which each lattice site is equipped with a voltage‑dependent capacitor realized by a common‑cathode diode. The capacitance follows C(v)=C_L