Topological boundary modes in nonlinear mechanical lattices

Mechanical lattices have been shown to possess interface modes lying in bulk band gaps. These boundary modes are protected by bulk topological invariants in which the geometric (Berry) phase is quantized by certain symmetries, the celebrated bulk-boundary correspondence. This relationship has been proved rigorously for linear mechanical systems, which can be mapped onto quantum systems, yet recent has demonstrated that the boundary modes extend into the nonlinear regime. In the present work, we investigate the topological protection of nonlinear normal modes. In particular, we consider a one-dimensional diatomic chain with spatial inversion symmetry, whose linear limit has a well-characterized topological invariant. By continuing the linear modes into the nonlinear regime via a mix of numerical and analytic methods, we characterize how nonlinear topological boundary modes emerge, paving the way to topological modes of strongly and inherently nonlinear systems.