Abstract
We show that topological interface mode can emerge in a one-dimensional elastic string system which consists of two periodic strings with different band topologies. To verify their topological features, Zak-phase of each band is calculated and reveals the condition of topological phase transition accordingly. Apart from that, the transmittance spectrum illustrates that topological interface mode arises when two topologically distinct structures are connected. The vibration profile further exhibits the non-trivial interface mode in the domain wall between two periodic string composites.
Highlights
Assuming that the entire structure is stretched by an external force to provide the tension, along the z-axis, we can write down the Lagrangian density for the string wave
The Zak phase plays an important role in the classification of topological insulators, insulators, and the interface mode arises around the domain role wall in of two topologically distinct band mentioned, the Zak phase anwall important the distinct classification of topological and theAs interface mode arises around the plays domain of two topologically band structures
System and reveal the topological phase transition arises from band crossing
Summary
The recent discovery of topological features in condensed matter systems [1,2,3,4,5,6,7,8], for example, chiral edge states [9,10,11] or effective magnetic fields [12] have attracted massive interests [13,14]. To study the band topology in a 1D periodic system with inversion symmetry, the Zak phase is introduced to facilitate the topological classification [2,19]. When two SSH chains with distinct staggered hopping are connected, interface states arise at the domain wall as long as the corresponding Zak phases for both subdomains are different. While the research to topological phenomena has been investigated in various classical wave models [29,30,31], topological properties of pre-tensioned strings remain unnoticed. Since the vibrating frequency and amplitude of a pre-tensioned string system can be measured, the system shows great potential to directly observe topological properties. The purpose of the study is to explore the topological phase transition in a 1D elastic string (ES) system through the analysis of the related topological interface mode.
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