Topological edge and corner states in non-Hermitian Lieb lattice elastic metamaterials supporting slow waves

The exploration of topological states in two-dimensional (2D) Bravais lattices under non-Hermitian conditions with gain and loss mechanisms has become a dynamic frontier in physics and materials science, offering robust wave control and novel functionalities. The Lieb lattice system features dispersionless flat bands intersecting at Dirac points, which exhibit unique slow-wave characteristics that distinguish it from other Bravais lattices and enable flexible wave manipulation. However, existing research on topological states in Lieb lattices primarily focuses on Hermitian photonic crystals and phononic crystals, the realization of non-Hermitian topological states with slow-wave propagation characteristics in elastic Lieb lattice systems remains notably scarce. Here, we propose a 2D phononic crystal plate constructed with a Lieb lattice to realize topological edge and corner states of flexural waves under both Hermitian and non-Hermitian modulation. By introducing two inversion-related dimerization configurations into the Lieb lattice, the bulk band degeneracies are lifted, leading to topological flat-band 2 edge states and corner states at the interface between the two configurations. Furthermore, the introduction of non-Hermitian parameters through strategically distributed gain and loss into the two inversion-related dimerization configurations induces exceptional points (EPs), giving rise to edge and corner states with non-Hermitian characteristics. Finally, topological slow-wave propagation with suppressed backscattering under disorders and bends in both Hermitian and non-Hermitian system is demonstrated. These results establish a new paradigm for achieving non-Hermitian slow-wave transmission and higher-order topological energy localization in Lieb lattices, with direct potential for applications in slow-wave-based elastic energy harvesting and signal sensing.