Landau-Zener Effect Induced Hysteresis in Topological Josephson Junctions.

In topological Josephson junctions, Majorana zero modes form a quantum two-level system which provides a natural platform for the interplay between the Josephson effect and Landau-Zener effect. To study this interplay, we extend the standard resistively and capacitively shunted junction model by including the internal quantum degree of freedom from the two levels. We obtain hysteresis in the I-V characteristics with a mechanism entirely different from the conventional junctions. In particular, this hysteresis exists even in extremely overdamped junctions, which agrees with recent unusual experimental findings. We also demonstrate a mapping from the quantum dynamics to a purely classical nonlinear dynamics in a restricted three-dimensional phase space, where the hysteresis can be understood as coming from the different static and kinetic dry friction. Further investigations in a corresponding topological SQUID reveal interference patterns with periods $h/e$ and $h/2e$ for the switching and retrapping current respectively.