Transport theory for topological Josephson junctions with a Majorana qubit

Abstract

We construct a semiclassical theory for the transport of topological junctions starting from a microscopic Hamiltonian that comprehensively includes the interplay among the Majorana qubit, the Josephson phase, and the dissipation process. With the path integral approach, we derive a set of semiclassical equations of motion that can be used to calculate the time evolution of the Josephson phase and the Majorana qubit. In the equations we reveal rich dynamical phenomena such as the qubit induced charge pumping, the effective spin-orbit torque, and the Gilbert damping. We demonstrate the influence of these dynamical phenomena on the transport signatures of the junction. We apply the theory to study the Shapiro steps of the junction, and find the suppression of the first Shapiro step due to the dynamical feedback of the Majorana qubit.

arXiv comment6 pages, 3 figures

References in corpus (51)

• Fault-tolerant quantum computation by anyons
• Unpaired Majorana fermions in quantum wires
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• Quantum state engineering with Josephson-junction devices
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Superconducting Qubits: Current State of Play
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• Landau-Zener-Stuckelberg interferometry
• Evidence of topological superconductivity in planar Josephson junctions
• $4\pi$-periodic Josephson supercurrent in HgTe-based topological Josephson junctions
• Fractional ac Josephson effect in p- and d-wave superconductors
• Topological Superconductivity in a Phase-Controlled Josephson Junction
• Gapless Andreev bound states in the quantum spin Hall insulator HgTe
• Helical Topological Edge States in a Quadrupole Phase
• Josephson radiation from gapless Andreev bound states in HgTe-based topological junctions
• Dynamical detection of Majorana fermions in current-biased nanowires
• Phase signature of topological transition in Josephson Junctions
• Observation of the 4$\pi$-periodic Josephson effect in indium arsenide nanowires
• Majorana splitting from critical currents in Josephson junctions
• $4\pi$ periodic Andreev bound states in a Dirac semimetal
• Decoherence of superconducting qubits caused by quasiparticle tunneling
• Microwave Spectroscopy Reveals the Quantum Geometric Tensor of Topological Josephson Matter
• Josephson supercurrent through the topological surface states of strained bulk HgTe
• Josephson junction dynamics in the presence of $2\pi$- and $4\pi$-periodic supercurrents
• Fractional Josephson Vortices and Braiding of Majorana Zero Modes in Planar Superconductor-Semiconductor Heterostructures
• Quantum-Dot Parity Effects in Trivial and Topological Josephson Junctions
• Joule overheating poisons the fractional ac Josephson effect in topological Josephson junctions
• Parity-controlled $2\pi$ Josephson effect mediated by Majorana Kramers pairs
• Detecting topological superconductivity using low-frequency doubled Shapiro steps
• Parity anomaly and spin transmutation in quantum spin Hall Josephson junctions
• Anomalous Floquet Chiral Topological Superconductivity in a Topological Insulator Sandwich Structure
• Ultrathin Films of Superconducting Metals as a Platform for Topological Superconductivity
• Conductance spectroscopy of nontopological-topological superconductor junctions
• Superconducting islands with semiconductor-nanowire-based topological Josephson junctions
• Majorana-Josephson Interferometer
• Transport in superconductor--normal metal--superconductor tunneling structures: Spinful p-wave and spin-orbit-coupled topological wires
• Doubled Shapiro Steps in a Topological Josephson Junction
• Quasiparticle poisoning effects on the dynamics of topological Josephson junctions
• Hysteresis from nonlinear dynamics of Majorana modes in topological Josephson junctions
• Anomalous modulation of Josephson radiation in nanowire-based Josephson junctions
• Voltage staircase in a current-biased quantum-dot Josephson junction
• Majorana-induced DC Shapiro steps in topological Josephson junctions
• Thermodynamics in topological Josephson junctions
• Josephson radiation from nonlinear dynamics of Majorana zero modes
• Critical current for an insulating regime of an underdamped current-biased topological Josephson junction
• Chiral topological superconductivity in Josephson junction
• Non-adiabatic Josephson Dynamics in Junctions with in-Gap Quasiparticles
• Reentrance effect in macroscopic quantum tunneling and non-adiabatic Josephson dynamics in d-wave junctions

Cited by in corpus (2)

• Fractional Josephson effect versus fractional charge in superconducting-normal metal hybrid circuits
• Time-dependent driving and topological protection in the fractional Josephson effect