Two classes of topological acoustic crystals - Yang, Zhaoju (2017)
This thesis studies two classes of unconventional acoustic crystals. The first class of the acoustic crystal is a two-dimensional crystal with topologically gapped band structure. Circulating flow is introduced into each unit cell to play the role of vector potential. We present a theoretical model to characterize the underlying physics – quantum Hall effect for acoustics. Through numerical calculation, we show that the nontrivial band gap emerges and the band below the gap acquires a non-zero Chern number. As a result, the non-reciprocal acoustic crystal exhibits a topologically protected one-way edge state inside the band gap. The second class of the acoustic crystal is a three-dimensional and gapless crystal. The isolated degenerate points, which are known as type-II Weyl nodes in three- dimensional momentum space, indicate the existence of topological transition and acquire non-zero Chern number. The Weyl nodes are rather robust against perturbations and annihilate only in pairs of opposite chirality. In addition, the topological Fermi-arc- like surface states can be traced out as an analogue of Fermi arcs as in condensed matter physics. Last but not least, we demonstrate the unique features of the acoustic type-II Weyl system, such as a finite density of states, transport properties of the surface states.