Hysteresis from nonlinear dynamics of Majorana modes in topological Josephson junctions
arXiv:1801.05099 · doi:10.1103/PhysRevB.98.134515
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 and in topological superconducting quantum interference devices.
arXiv comment17 pages, 11figures
References in corpus (53)
- Topological insulators and superconductors
- Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
- Unpaired Majorana fermions in quantum wires
- Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
- Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
- Helical liquids and Majorana bound states in quantum wires
- New directions in the pursuit of Majorana fermions in solid state systems
- Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
- A generic new platform for topological quantum computation using semiconductor heterostructures
- Periodic table for topological insulators and superconductors
- Search for Majorana fermions in superconductors
- Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
- NMR Techniques for Quantum Control and Computation
- Exponential Protection of Zero Modes in Majorana Islands
- Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
- Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
- Landau-Zener-Stuckelberg interferometry
- Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
- Topological Superconductivity and Superfluidity
- Manipulation of Majorana fermion, Andreev reflection and Josephson current on topological insulators
- Milestones toward Majorana-based quantum computing
- Majorana Fermions in Semiconductor Nanowires: Fundamentals, Modeling, and Experiment
- Splitting of a Cooper pair by a pair of Majorana bound states
- AC JOSEPHSON EFFECT IN A SINGLE QUANTUM CHANNEL
- Light-field driven currents in graphene
- -periodic Josephson supercurrent in HgTe-based topological Josephson junctions
- Fractional ac Josephson effect in p- and d-wave superconductors
- Majorana qubit decoherence by quasiparticle poisoning
- Theory of nonlinear Landau-Zener tunneling
- Edge-mode Superconductivity in a Two Dimensional Topological Insulator
- AC Josephson effect in finite-length nanowire junctions with Majorana modes
- Adiabatic Theory of Nonlinear Evolution of Quantum States
- Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
- Dynamical detection of Majorana fermions in current-biased nanowires
- Many-body Landau-Zener dynamics in coupled 1D Bose liquids
- Coulomb stability of the 4π-periodic Josephson effect of Majorana fermions
- Majorana splitting from critical currents in Josephson junctions
- Characterization of Qubit Dephasing by Landau-Zener Interferometry
- Detecting Topological Phases in Cold Atoms
- All Majorana Models with Translation Symmetry are Supersymmetric
- Signatures of topological Josephson junctions
- Decoherence of Majorana qubits by noisy gates
- Josephson supercurrent through the topological surface states of strained bulk HgTe
- Superconducting Memristors
- A survey of classical and quantum interpretations of experiments on Josephson junctions at very low temperatures
- The Realization and Dectection of Weyl Semimetals and Chiral Anomaly in Cold Atomic Systems
- Splitting and oscillation of Majorana zero modes in the p-wave BCS-BEC evolution with plural vortices
- Superconducting single-mode contact as a microwave-activated quantum interferometer
- Qubit-based memcapacitors and meminductors
- Solitonic Josephson-based meminductive systems
- Optimizing the Majorana character of SQUIDs with topologically non-trivial barriers
- Manipulating the Majorana Qubit with the Landau-Zener-Stückelberg Interference
- Supersymmetry in Closed Chains of Coupled Majorana Modes
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