Nonlinear quadrupole topological insulators

TL;DR

This paper introduces nonlinear quadrupole topological insulators (NLQTIs), demonstrating their experimental realization in electric circuits and revealing unique nonlinear topological states and solitons in various regimes.

Contribution

It proposes the concept of NLQTIs, extends HOTIs into the nonlinear regime, and experimentally demonstrates their unique topological and solitonic phenomena in electric circuits.

Findings

Observation of nonlinear topological corner states.

Identification of bulk solitons in different nonlinear regimes.

Experimental realization of NLQTIs in electric circuit lattices.

Abstract

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.