Tunable Topological Phononic Crystals

Abstract

Topological insulators first observed in electronic systems have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial band gaps. Such band gaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topological transition that we verify by the Chern number calculation and edge-mode analysis. We develop a complete model based on the tight binding to uncover the physical mechanisms of the topological transition. Both the model and numerical simulations show that the topology of the band gap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.

Snowflake phononic topological insulator at the nanoscale

“…So far, experimental implementations exist on the centimeter scale, both for the case of time-reversal symmetry broken by external driving [1], such as in coupled gyroscopes, as well as for the case without driving [2][3][4][5][6], such as in coupled pendula. Moreover, a multitude of different implementations have been envisioned theoretically [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. However, it is highly desirable to come up with alternative design ideas that may be realized on the nanoscale, eventually pushing towards applications in integrated phononics.…”

Topological helical edge states in water waves over a topographical bottom

“…Topology was originally an abstract concept in mathematics but in recent decades has gradually found to be closely related to many interesting physical phenomena not only in electronic systems including the quantum Hall (QH) effect and quantum spin Hall (QSH) effect [4][5][6][7], but also in classical wave systems such as photonic and acoustic crystals [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. However, the relevant study in the field of water waves [1][2][3][26][27][28][29][30][31][32][33][34][35][36][37][38][39] is very limited.…”

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

“…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.…”

“…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. 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].…”