Self-Induced Dirac Boundary State and Digitization in a Nonlinear Resonator Chain

The low-energy excitations in many condensed matter and metamaterial systems can be well described by the Dirac equation. The mass term associated with these collective excitations, also known as the Dirac mass, can take any value and is directly responsible for determining whether the resultant band structure exhibits a band gap or a Dirac point with linear dispersion. Manipulation of this Dirac mass has inspired new methods of band structure engineering and electron confinement. Notably, it has been shown that a massless state necessarily localizes at any domain wall that divides regions with Dirac masses of different signs. These localized states are known as Jackiw-Rebbi-type Dirac boundary modes and their tunability and localization features have valuable technological potential. In this study, we experimentally demonstrate that nonlinearity within a 1D Dirac material can result in a self-induced domain boundary for the Dirac mass. Our experiments are performed in a dimerized magnetomechanical metamaterial that allows complete control of both the magnitude and sign of the local material nonlinearity, as well as the sign of the Dirac mass. We find that the massless bound state that emerges at the self-induced domain boundary acts similarly to a dopant site within an insulator, causing the material to exhibit a dramatic binary switch in its conductivity when driven above an excitation threshold.