Nonlinear corner states in topologically trivial and nontrivial Kagome lattice

Just as topological insulator has revolutionized the understanding of electronic systems, topological mechanics is bringing a fresh perspective to the world of mechanical systems. It explores how the elegant concepts of topology can be harnessed to manipulate the mechanical behaviour of materials. In recent times, there has been a surge of research in this field, shedding light on the robust propagation of waves within materials. However, a significant portion of these research studies has primarily focused on linear dynamics. Our present work represents a significant step towards understanding the intricate interplay between nonlinearity and topology within mechanical systems. In particular, we investigate a mechanical Kagome lattice that is known to support higher-order topological states, i.e., corner states. We show that by introducing an onsite nonlinearity, the corner state in a topologically nontrivial lattice can be tuned in frequency and stability. Interestingly, we find new families of corner states that do not exist in the linear Kagome lattice. Moreover, nonlinearity also enables us to discover corner states in topologically trivial lattices. The findings highlight the effect of nonlinearity on the characteristics of topologically robust corner states and the existence of whole new families of corner states that are not present in linear lattices.