Floquet Topological Insulators (FTIs) have inspired analogues in photonics, optics, and acoustics, in which non-reciprocal wave propagation in topologically protected materials, with topological immunity against structural defects and disorder, is achieved due to the breaking of time-reversal symmetry induced by time-modulation. This study aims at investigating a possibility for the existence of a mechanical analogue to the Quantum Hall Effect (QHE) in one and two-dimensional periodically modulated lattices. In 1D, the system shows topologically protected one-way edge modes as the time-modulation is turned on, which is demonstrated by the principle of bulk-edge correspondence and transient numerical simulations. The study is then extended to 2D hexagonal lattices to demonstrate the existence of Floquet topological edge modes. The band diagram and helical edge states characteristic of QHE are obtained by using the Plane Wave Expansion (PWE) method. Given the breakage of the time-reversal symmetry, the system switches from the trivial state to the nontrivial topological one that is quantified in terms of topological invariant Chern numbers. Last, the robustness of one-way edge modes and their immunity to backscattering by sharp corners, defects and modulation disorders are analyzed and assessed numerically.

Date Published: 1 April 2019
PDF
Proc. SPIE 10972, Health Monitoring of Structural and Biological Systems XIII, 1097219 (1 April 2019); doi: 10.1117/12.2514367

Published in SPIE Proceedings Vol. 10972:
Health Monitoring of Structural and Biological Systems XIII
Paul Fromme; Zhongqing Su, Editor(s)