Landau-Zener Effect Induced Hysteresis in Topological Josephson Junctions.
We reveal that topological Josephson junctions provide a natural platform for the interplay between the Josephson effect and LZ effect through a two-level system formed by coupled Majorana modes. We build a quantum resistively shunted junction model (QRSJ) by including the quantum two levels into the standard RSJ model. We obtain hysteresis in the I-V characteristics which exists in the overdamped regime while the hysteresis is not available when the LZ effect is absent. Our results can explain the unexpected hysteresis found in recent experiments. 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.
Publisher URL: http://arxiv.org/abs/1801.05099
DOI: arXiv:1801.05099v2
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