Hysteresis from nonlinear dynamics of Majorana modes in topological Josephson junctions

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 Schrödinger 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.

17 pages, 11figures

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Cited by in corpus (13)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Quasiparticle poisoning effects on the dynamics of topological Josephson junctions
• New types of topological superconductors under local magnetic symmetries
• Voltage staircase in a current-biased quantum-dot Josephson junction
• Majorana-induced DC Shapiro steps in topological Josephson junctions
• Josephson radiation from nonlinear dynamics of Majorana zero modes
• Microscopic theory of the current-voltage characteristics of Josephson tunnel junctions
• Critical current for an insulating regime of an underdamped current-biased topological Josephson junction
• Electromotive force in driven topological quantum circuits
• Transport theory for topological Josephson junctions with a Majorana qubit
• Time-dependent driving and topological protection in the fractional Josephson effect
• Josephson radiation patterns in underdamped topological Josephson junctions