Active topological phase transitions in high-order elastic topological insulators driven by pneumatic methods and liquid metals

Active topological phase transitions widely occur in active matters and biological systems, such as developing embryos. Since the discovery of the intriguing bulk-boundary effects of topological insulators in Hermitian and non-Hermitian systems, various electric, optical, acoustic, and mechanical topological metamaterials with efficient energy transmission and robust defect-immunization have been designed. To date, however, it remains a challenge to precisely and fast manipulate the topological phase transitions in elastic topological insulators. In this paper, on the basis of theoretical analysis and numerical simulations, we propose an active strategy to achieve this aim through a combination of pneumatic actuation and liquid metals. The proposed method can precisely tune the connecting stiffness and vertex mass in the tight Su-Schrieffer-Heeger model. Thus, we realize the effective and fast control of topological phase transitions and elastic wave bandgap switching. We also uncover the active spinning bulk-boundary effects and higher-order topological states in the elastic topological insulators, demonstrating the high effectiveness and practicability of the proposed method. In addition, the differences between the 1D edge and 0D corner higher-order states are specified by information entropy theory. This work not only gains insights into the active manipulation of topological phase transitions but also inspires novel strategies to design active topological materials through untethered methods, e.g., magnetism or biological cells.