Soft topological modes protected by symmetry in rigid mechanical metamaterials

Topological mechanics can realize soft modes in mechanical metamaterials which the number of degrees freedom for particle motion is finely balanced by constraints provided interparticle interactions. However, solid objects are generally hyperstatic (or overconstrained). Here, we show how symmetries may be applied to generate topological even overconstrained, rigid systems. To do so, consider non-Hermitian topology based on nonsquare matrices, and design a material low-energy protected symmetry appear at interfaces. Our approach presents novel way generating softness robust scale-free architectures suitable miniaturization nanoscale.