Corner states in a second-order acoustic topological insulator as bound states in the continuum

Abstract

A second order topological insulator is designed on a platform of a twodimensional (2D) square lattice with all coupling coefficients being positive. Simulated results show the existence of two types of nontrivial corner states in this system, with one type being identified as bound states in the continuum (BIC). The non-BIC corner states are also found by surrounding a nontrivial sample with a trivial one, and interestingly, these perfectly confined corner states can be gradually delocalized and merge into edge states by tuning the inter-system coupling coefficient. Both BIC and non-BIC corner states are originated from bulk dipole moments rather than the quantized quadrupole moments, with the corresponding topological invariant being the 2D Zak phase. Full wave simulations based on realistic acoustic waveguide structures are demonstrated. Our proposal provides an

Bound states in the continuum of higher-order topological insulators

“…The recent work of Ref. 66 introduces unrestricted (i.e., symmetry-breaking) noise to their system. Thus, we expect that their numerical method for finding corner-localized states is incapable of properly distinguishing BICs from resonances.…”

Simulating Floquet topological phases in static systems

“…Systems with gapless corner modes have successfully been realized in many different platforms [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50], most of them being the classical analogs of condensed matter systems. Even though such realizations offer a better control over disorder, its complete elimination remains a challenging task.…”

“…The method relies on two parts: (1) constructing a HOTI and (2) measuring the eigenphases of its reflection matrix. The first part has already been achieved in photonic [35][36][37], phononic [38], microwave [39], acoustic [41][42][43][44][45][46][47]50], topoelectric [40], and condensed-matter [49] metamaterials, producing HOTI Hamiltonians similar to Eq. (1).…”

“…The required ingredients, a HOTI probed by means of a scattering measurement, are presently available in the lab. HOTIs have been achieved in a variety of metamaterials [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. The reflection matrix can be determined by standard interferometric techniques [51,52], or by simply visualizing the standing wave pattern formed between incoming and outgoing modes [49,53].…”

Simulation of topological phases with color center arrays in phononic crystals

“…For the generalized SSH Hamiltonian, the interaction between different sites of a 1D chain is described by the alternating off-diagonal elements. Due to the intrinsic topological features of the SSH model, various quantum systems are employed to simulate the SSH model, and to explore interesting applications in quantum information processing [12][13][14][15][16][17][18][19][20][21][22][23][24]. However, the simulation of topological phenomena in the quantum domain is still challenging in practice due to stringent conditions.…”