Exceptional rings protected by emergent symmetry for mechanical systems

We propose mechanical systems, described by Newton's equation of motion, as suited platforms for symmetry protection of non-Hermitian topological degeneracies. We point out that systems possess emergent symmetry, which is a unique properties of mechanical systems. Because of the emergent symmetry, in contrast to other systems, fine-tuning of parameters (e.g., gain and loss) is not required to preserve the symmetry protecting exceptional rings in two dimensions. The presence of symmetry-protected exceptional rings (SPERs) in two dimensions is numerically demonstrated for a mechanical graphene with friction. Furthermore, classification of symmetry-protected non-Hermitian degeneracies is addressed by taking into account the above special characteristics of mechanical systems.