Robust gapless edge states and unconventional topological band properties in a two-dimensional elastic Kekulé phononic lattice

The existence of back-scattering-immune edge states in topological metamaterials has opened a new path for mechanical waveguide design. Recently, a “Brillouin-zone-folding" strategy was proposed to easily realize non-trivial topological properties in two-dimensional phononic systems. However, due to the intrinsic characteristics of phonons, the resulting edge states are generally gapped, indicating coupling between counter-propagating edge states. We report on the design of an elastic phononic structure that embeds a Kekulé distortion pattern to create the analogue of a quantum spin Hall system which, with proper tuning, can achieve fully decoupled and gapless edge states. Using ab initio numerical calculations, we also discover unconventional characteristics of the phononic band structure including a six-lobe pseudospin texture and Berry curvature. We also find that the existence of edge-states does not depend exclusively on the topological invariants of the adjacent bulk lattices but also on the relative translation of the unit cell pattern, therefore it is possible to obtain edge states on an edge dislocation of one bulk lattice.