Abstract
Topological mechanics is rapidly emerging as an attractive field of research where mechanical waveguides can be designed and controlled via topological methods. With the development of topological phases of matter, recent advances have shown that topological states have been realized in the elastic media exploiting analogue quantum Hall effect, analogue quantum spin Hall effect, analogue quantum valley Hall effect, higher-order topological physics, topological pump, topological lattice defects and so on. This review aims to introduce the experimental and theoretical achievements with defect-immune protected elastic waves in mechanical systems based on the abovementioned methods, respectively. From these discussions, we predict the possible perspective of topological mechanics.
Highlights
We have shown the breakthroughs in this research field made in recent years
We can regulate the elastic waves in different topological protection methods
The development of topological physics in mechanical systems still lag behind the electronic, photonic and acoustic systems. We will outline those future developments of topological mechanics as follows: (1)
Summary
In 1982, Thouless et al explored the mechanism of the integer quantum Hall effect and elucidated the relationship between the integer in the Hall conductance and a topological invariant in the QHE system [2] They proposed the TKNN (Thouless–Kohmoto–Nightingale–den Nijs) theory to define the integer, namely the Chern number. Realizing QSHE exploits the spin-orbit interactions and time-reversal symmetry In these systems, a Chern number of zero arose from the existence of conjugate electronic spins, the topological nature is characterized by a Z2 topological invariant or the spin Chern number [7,8]. The abovementioned distinct topological states could be realized in classical systems, such as photonics, acoustics, mechanics, electric circuits and so on since the topological nature is unrelated to the quantum characteristics and depends on the wave characteristics [30].
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