Higher-order topological insulator in a spring-mass system

Abstract

Abstract Higher-order topological insulators (HOTIs) have attracted much attention in various fields in the recent years. In this work, we propose a two-dimensional (2D) square lattice spring-mass model, where restoring forces between nearest neighbors can be induced by either longitudinal or transverse vibrations. Edge states exist on the interface between topological nontrivial and trivial lattices, and two different types of corner states are identified. The proposed spring-mass model has plenty of degrees of freedoms (DOFs), including both longitudinal and transverse spring constants as well as the mass of each particle. It turns out that edge and corner states with flexible spatial distributions can be realized by slightly tuning the elastic and inertial parameters. A lot of interesting topological patterns such as edge states along 4, 2, or only 1 edge, and second-order corner states around 4, 2, or 1 corner are unambiguously demonstrated. Our work provides an easy-to-tune platform to realize HOTIs, which is useful when multipole bulk polarizations or negative couplings are absent or difficult to realize. Classical spring-mass models governed by Newton's laws also have the advantage of superior controllability and feasible experimental implementability.