Experimental demonstration of anomalous Floquet topological insulator for sound

Abstract

Time-reversal invariant topological insulator is widely recognized as one of the fundamental discoveries in condensed matter physics, for which the most fascinating hallmark is perhaps a spin-based topological protection, the absence of scattering of conduction electrons with certain spins on matter surface. Recently, it has created a paradigm shift for topological insulators, from electronics to photonics, phononics and mechanics as well, bringing about not only involved new physics but also potential applications in robust wave transport. Despite the growing interests in topologically protected acoustic wave transport, T-invariant acoustic topological insulator has not yet been achieved. Here we report experimental demonstration of anomalous Floquet topological insulator for sound: a strongly coupled metamaterial ring lattice that supports one-way propagation of pseudo-spin-dependent edge states under T-symmetry. We also demonstrate the formation of pseudo-spin-dependent interface states due to lattice dislocations and investigate the properties of pass band and band gap states.

Topological characterization of chiral models through their long time dynamics

“…The expressions (20) and (21) are invariant under the change of j to j -, as the skew polarization is invariant under such change. Therefore, we can compute the traces over all the  chiral localized states:…”

“…In the figure we also show a sliding average of the data over ten points (orange curve), which shows a smoother and quicker convergence to the winding number. Finally, let us note that the simplest procedure which yields the desired result (the winding) is to follow equation (20) and take the sum of the mean displacement measured over two orthogonal states which are completely localized on the central unit cell, and which form a complete basis of the left sublattice (the one corresponding to the +1 eigenvalue of the chiral operator). Minus two times this quantity will give the result plotted in figure 3 …”

“…A famous example of this correspondence can be found in the Quantum-Hall effect where the quantization of the Hall conductance is rooted in the current-carrying protected edge states [3][4][5]. The ensemble of (natural and artificial) topological insulators is steadily growing, and these have been by now synthetically engineered in a multitude of physical systems such as atomic [6][7][8][9][10][11], superconducting [12], photonic [13][14][15][16][17] and acoustic platforms [18][19][20].This work focuses on one-dimensional (1D) topological insulators possessing chiral symmetry. As a consequence of the chiral symmetry, the different sites of the unit cell can always be regarded as part of two sublattices.…”

Experimental verification of acoustic pseudospin multipoles in a symmetry-broken snowflakelike topological insulator

“…To resolve this obstacle, analogous unidirectional edge channels have been demonstrated in phononic crystals (PnC), which were constructed with circulating flow fields [18][19][20][21]37] to break the time-reversal symmetry to mimic the QHE. Similarly, coupled ring resonator waveguides were proposed analogous to a Floquet insulator [23][24][25]. Beyond that, valley-projected acoustic topological insulators were proposed to obtain backscattering-immune valley transport [30,32].…”

“…Topological states have also been extended to condensed-matter physics based on the quantum Hall effect (QHE) [1,2], the quantum spin Hall effect (QSHE) [3,4], and topological insulators (TIs) [5,6]. Over the past ten years, investigation into new topologically protected edge states has started to grow in other subfields of physics, such as photonics [7][8][9][10][11][12][13][14][15][16], phononics [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], and mechanics [33][34][35][36]. The intrinsic difference between electrons and acoustic waves represents a great challenge in creating the spinlike degree of freedom for sound only possessing longitudinal polarization.…”