Majorana-like topologically bound states with self-replicating features in elastic structures

Abstract

In analogy to the Majorana bound state in superconductor electronic systems, a new type of zero-order topological state called Dirac-vortex state has recently been implemented in the photonic and phononic communities as a new strategy to provide tight and robust confinement of classical waves. In the realm of elastic waves, these Majorana-like bound state have been demonstrated as a potential candidate for designing efficient energy harvesting devices. However, previous demonstrations of the Dirac-vortex states are primarily limited to a single frequency (i.e., fixed at a single mid-gap Dirac frequency), which restricts their applicability in scenarios requiring multi-working frequencies. Here, we propose a Kekulé-modulated elastic lattice structure, engineered from fixed-free beams coupled through slender rods, which supports Majorana-like elastic wave topologically bound states spanning multiple frequency ranges. Through a combination of theoretical beam-spring modeling and finite element simulations, multiple Dirac-vortex modes with self-replicating properties are comprehensively confirmed through the analysis of bandstructure and examination of eigenspectra. We present convincing evidence for the high localization and robust confinement of these multi-frequency Dirac-vortex states, which are the key features of nontrivial Majorana-like bound states. The proposed structure, composed of ubiquitous mechanical elements, provides a platform for potential applications such as multi-frequency energy harvesting, on-chip communication, and seismic wave remote sensing.