Topological Phase Transition in a One-Dimensional Elastic String System
Ya-Wen Tsai1,2*, Yao-Ting Wang1, Pi-Gang Luan2, Shuang Zhang1
1School of Physics and Astronomy, University of Birmingham, Birmingham, UK
2Department of Optics and Photonics, National Central University, Jhongli, Taiwan
* presenting author:Yawen Tsai,
We show that topological phase transition can occur in a one-dimensional elastic string system. The system consists of two subsystems of periodic strings connected at the interface, each has binary type unit cell of two materials. For any one of them, varying the density and controlling the segment lengths of the materials in one unit cell continuously, band crossing can happen, accompanying with the switch of the Zak phases [1] for the two bands just below and above a gap. The switching of Zak phases for the two bands implies that if the material parameters of the two subsystems correspond to two sets of the tuning parameters mentioned above, one before and the other after the switching, respectively, then the interface impedances of the two subsystems must be of opposite signs when they share a common gap while the interface state appears [2].
We study the vibration feature of this combined string system by setting a continuous wave source on one side of the total system and excite the string. A narrow peak of transmittance appears in the gap around the reduced frequency 2.8, which indicates the existence of an interface state. Our study demonstrates that topological phase transition can be found in a one-dimensional elastic string system consisting of realistic materials which is possible to be designed and tested in practice.

[1] J. Zak, Berry’s Phase for Energy Bands in Solids, Phys. Rev. Lett. 62, 2747 (1989).
[2] M. Xiao, Z. Q. Zhang, and C. T. Chan, Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems, Phys. Rev. X 4, 021017 (2014).

Keywords: Zak phase, Topological phase transition, Elastic string, Impedance