Josephson radiation from nonlinear dynamics of Majorana modes in topological Josephson junctions*

Recently, in topological Josephson junctions, the electromagnetic emission with the quantized frequency of eV/h has been experimentally observed as a consequence of the 4π-periodic Josephson effect, showing a phase-sensitive signature of Majorana zero modes. However, experiments show that this nontrivial radiation vanishes above a critical voltage, sharply contradicting previous theoretical results of the standard resistively shunted junction model. We extend this model to include the Majorana dynamics and show a quantitative agreement with the experimental results. Furthermore, we predict a fragment emission line and a chaos regime which can be observed experimentally by altering the junction parameters. We reveal that all these unique features come from the nonlinear dynamics of Majorana zero modes. The fragmental emission line and its vanishment are well explained with a fixed-point portrait, while the chaotic behavior is understood as the result of the bifurcation of fixed points. Our work will inspire more works to examine the structure of the radiation spectrum of topological Josephson junctions, which is wildly presented in experimental devices.