Realization of the Square-Root Higher-Order Topological Insulator in Electric Circuits

Abstract

Higher-order topological insulator (HOTI) represents a new phase of matter, the characterization of which goes beyond the conventional bulk-boundary correspondence and is attracting significant attention by the broad community. Using a square-root operation, it has been suggested that a square-root HOTI may emerge in a hybrid honeycomb-kagome lattice.Here, we report the first experimental realization of the square-root HOTI in topological LC circuits. We show theoretically and experimentally that the square-root HOTI inherits the feature of wave function from its parent with corner states pinned to nonzero energies. The topological feature is fully characterized by the bulk polarization. To directly measure the finite-energy corner modes, we introduce extra grounded inductors to each node, which shifts corner states to zero-energy without affecting their spatial distributions. Our results experimentally substantiate the emerging square-root HOTI and pave the way to realizing exotic topological phases that are challenging to observe in condensed matter physics.

Unconventional node voltage accumulation in generalized topolectrical circuits with multiple asymmetric couplings

“…Interestingly, with proper tuning of the coupling capacitors, the model circuit with 4-node unit cells depicted in Fig. 1c can be transformed to a square-root topological lattice [34,[65][66][67] whose parental topological insulator corresponds to the 2-node circuit of Fig. 1a.…”

“…While the BBC can already be broken with a single asymmetric non-Hermitian coupling, the more interesting interplay between multiple asymmetric non-Hermitian couplings has not been thoroughly explored. The interplay of multiple dissimilar and possibly asymmetric couplings becomes especially physically relevant in the topolectrical (TE) circuit [29][30][31][32][33][34][35][36][37][38] context, where circuit connections can be engineered and reconfigured in arbitrarily complicated manners. A variety of novel phenomena associated with non-Hermitian systems has generated much recent interest for novel applications such as ultra-sensitive sensors [39,40], quantum computations [41][42][43], quantum Hall states [42,[44][45][46][47], and reflectionless transmitters [48,49].…”

Square-root topological phase with time-reversal and particle-hole symmetry

“…After this proposal, analysis of square-root topological insulators in higher dimensions has been addressed [25][26][27][28][29][30][31][32] , which has elucidated ubiquity of the squareroot topological phases. For instance, a square-root counterpart of higher-order topological phases are reported by both theoretical 25 and experimental works 33,34 . In addition, Refs.…”

Second‐Order Photonic Topological Corner States in Square Lattices with Low Symmetry

“…As novel topological phases, higher-order topological insulating (HOTI) phases have recently been discovered in various quantum and classical systems, including crystalline [19] and amorphous materials, [20,21] photonic [15,16,[22][23][24][25][26][27][28][29][30][31] and phononic The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/andp.202100075 DOI: 10.1002/andp.202100075 crystals, [32][33][34][35] and electric circuits. [36,37] As one of the most well-known and simplest second-order topological insulator (SOTI), one might take the SOTI in the systems described by 2D SSH model (see, e.g., ref. [15]).…”