Hysteresis from nonlinear dynamics of Majorana modes in topological Josephson junctions

TL;DR

This paper explores how Majorana modes in topological Josephson junctions cause hysteresis in I-V curves through nonlinear dynamics, providing insights into experimental observations and interference patterns.

Contribution

It introduces a modified RSJ model incorporating Majorana-induced two-level systems and analytically demonstrates their nonlinear dynamics causing hysteresis.

Findings

Hysteresis explained by nonlinear Majorana dynamics

Coexistence of $h/e$ and $h/2e$ interference patterns predicted

Analytical solutions match recent experimental results

Abstract

We reveal that topological Josephson junctions provide a natural platform for the interplay between the Josephson effect and the Landau-Zener effect through a two-level system formed by coupled Majorana modes. We build a quantum resistively shunted junction (RSJ) model by modifying the standard textbook RSJ model to take account of the two-level system from the Majorana modes at the junction. We show that the dynamics of the two-level system is governed by a nonlinear Schr\"odinger equation and solve the equations analytically via a mapping to a classical dynamical problem. This nonlinear dynamics leads to hysteresis in the I-V characteristics, which can give a quantitative explanation to recent experiments. We also predict the coexistence of two interference patterns with periods $h/e$ and $h/2e$ in topological superconducting quantum interference devices.