Non-reciprocal matter is a special type of active matter in which basic principles like Newton’s 3rd law and the Hermiticity of Hamiltonians are broken by design and where far-from-equilibrium phenomena like unidirectional wave amplification—the so-called non-Hermitian skin effect—emerge. While the linear response of these materials is by now well established, the nonlinear response remains largely uncharted. We don’t know yet how nonlinearities affect the nature and the characteristics of the waves propagating in non-reciprocal matter. We demonstrate experimentally, numerically and theoretically that non-reciprocal matter can host nonlinear excitations, breathers, that propagate unidirectionally. These one-way breathers naturally emerge without careful crafting of the initial conditions—which is usually required to observe breathers. Using perturbative methods, we demonstrate that such breathers have a memory of the initial condition and have a long time dynamics that is controlled by the interplay between non-reciprocity and dissipation.
