Topological Edge States in an Elastic Lieb Lattice

Flat-band systems, such as the Lieb lattice, are receiving growing interest due to the interplay between dispersionless and Dirac bands, which leads to intriguing wave dynamics and topological properties. Edge states can emerge in these periodic lattices, offering potential applications such as vibration isolation, waveguiding, and energy harvesting. While edge states have been reported in electronics, photonics, and acoustics, their elastic counterparts remain largely unexplored. In this work, we explore the emergence of edge states in a spring-mass Lieb lattice, where both nearest-neighbor and next-nearest-neighbor interactions are represented as springs connecting discrete masses. The edge state emergence is observed in lattices with significant next-nearest-neighbor interactions and appropriate masses dimerization. By exciting a square lattice at a point with a tone burst, our time-domain solution demonstrates perfect wave propagation along the edges, with negligible loss and reflection at the corners. These findings to be reported in this work open new avenues for designing robust elastic waveguides for vibration energy transport and management.