Designing topological interface states in phononic crystals based on the full phase diagrams

Yan Meng,Hong Xiang,Peng Hu,Ruo-Yang Zhang,Yingzhou Huang,Shuxia Wang,Weijia Wen,Xin Li,Xiaoxiao Wu,Lixin Ge,Dezhuan Han

doi:10.1088/1367-2630/aad136

Abstract

The topological invariants of a periodic system can be used to define the topological phase of each band and determine the existence of topological interface states within a certain bandgap. Here, we propose a scheme based on the full phase diagrams, and design the topological interface states within any specified bandgaps. As an example, here we propose a kind of one-dimensional phononic crystals. By connecting two semi-infinite structures with different topological phases, the interface states within any specific bandgap or their combinations can be achieved in a rational manner. The existence of interface states in a single bandgap, in all odd bandgaps, in all even bandgaps, or in all bandgaps, are verified in simulations and experiments. The scheme of full phase diagrams we introduce here can be extended to other kinds of periodic systems, such as photonic crystals and designer plasmonic crystals.

Highlights

The topological physics is growing rapidly in condensed matter physics, from quantum Hall effect [1] to topological insulators [2,3] and Weyl semimetals [4]
It is found that the band topology of this kind of systems can be characterized by Zak phases, which are quantized topological invariants as long as the unit cell possesses inversion symmetry [22]
The band structure of the 1D phononic crystals (PCs) with sound hard boundaries can be obtained by the transfer matrix method (TMM) [28, 29], cos(ka) where k is the Bloch wave vector, is the angular frequency, va is the sound speed in air (343 m/s), a is the lattice constant (a=dA+dB), and SA(B) rA2(B) is the crosssectional area for tube-A(B)

Summary

Introduction

The topological physics is growing rapidly in condensed matter physics, from quantum Hall effect [1] to topological insulators [2,3] and Weyl semimetals [4]. While Weyl semimetals possess Weyl nodes, which give rise to monopoles and anti-monopoles in the momentum space, and support topological Fermi-arc surface states These topological surface states appear at the interface of two insulators with different topological phases, and are robust against some local defects and immune from the back-scattering. In light of these advantages, recent discoveries of topological interface states have been extended to various physical branches, including photonics [5,6,7,8,9,10,11,12,13,14] and phononics [15,16,17,18,19,20]. The transmission spectra and spatial distributions of the pressure field for the interface states are measured and exhibit excellent agreement with the simulated results

Results

Discussion

Methods