Critical current for an insulating regime of an underdamped current-biased topological Josephson junction

Abstract

We study analytically an underdamped current-biased topological Josephson junction. First, we consider a simplified model at zero temperature, where the parity of the non-local fermionic state formed by Majorana bound states (MBSs) localized on the junction is fixed, and show that a transition from insulating to conducting state in this case is governed by single-quasiparticle tunneling rather than by Cooper pair tunneling in contrast to a non-topological Josephson junction. This results in a significantly lower critical current for the transition from insulating to conducting state. We propose that, if the length of the system is finite, the transition from insulating to conducting state occurs at exponentially higher bias current due to hybridization of the states with different parities as a result of the overlap of MBSs localized on the junction and at the edges of the topological nanowire forming the junction. Finally, we discuss how the appearance of MBSs can be established experimentally by measuring the critical current for an insulating regime at different values of the applied magnetic field.

References in corpus (50)

• Non-Abelian Anyons and Topological Quantum Computation
• 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
• New directions in the pursuit of Majorana fermions in solid state systems
• Search for Majorana fermions in superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Majorana fermions in a tunable semiconductor device
• Exponential Protection of Zero Modes in Majorana Islands
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Epitaxy of Semiconductor-Superconductor nanowires
• $4\pi$-periodic Josephson supercurrent in HgTe-based topological Josephson junctions
• Towards a realistic transport modeling in a superconducting nanowire with Majorana fermions
• Fractional ac Josephson effect in p- and d-wave superconductors
• Majorana qubit decoherence by quasiparticle poisoning
• Majorana box qubits
• Persistent current in superconducting nanorings
• AC Josephson effect in finite-length nanowire junctions with Majorana modes
• Parity lifetime of bound states in a proximitized semiconductor nanowire
• Quantized zero bias conductance plateau in semiconductor-superconductor heterostructures without non-Abelian Majorana zero modes
• Unconventional Josephson signatures of Majorana bound states
• Zero-energy Andreev bound states from quantum dots in proximitized Rashba nanowires
• Dynamical detection of Majorana fermions in current-biased nanowires
• Topological Josephson ${\varphi }_0$-junctions
• Failure of protection of Majorana based qubits against decoherence
• Evidence for an anomalous current phase relation in topological insulator Josephson junctions
• Transport signatures of quasiparticle poisoning in a Majorana island
• Electric-Field Induced Majorana Fermions in Armchair Carbon Nanotubes
• Universal Quantum Computation with Hybrid Spin-Majorana Qubits
• Distinguishing topological Majorana bound states from trivial Andreev bound states: Proposed tests through differential tunneling conductance spectroscopy
• Multiple Andreev reflection and critical current in topological superconducting nanowire junctions
• Anomalous Josephson current via Majorana bound states in topological insulators
• Phenomenology and Dynamics of Majorana Josephson Junction
• Quantifying wave-function overlaps in inhomogeneous Majorana nanowires
• Correlations between Majorana fermions through a superconductor
• Decoherence of Majorana qubits by noisy gates
• Zero-energy pinning of topologically-trivial bound states in multi-band semiconductor-superconductor nanowires
• Anomalous Josephson effect in semiconducting nanowires as a signature of the topologically nontrivial phase
• Spin-dependent coupling between quantum dots and topological quantum wires
• Majorana fermions in carbon nanotubes
• Suppression of the overlap between Majorana fermions by orbital magnetic effects in semiconducting-superconducting nanowires
• Majorana quasiparticles in semiconducting carbon nanotubes
• Detecting Topological Superconductivity with ${\phi }_0$ Josephson Junctions
• Lifetime of Majorana qubits in Rashba nanowires with non-uniform chemical potential
• Hysteresis from nonlinear dynamics of Majorana modes in topological Josephson junctions
• Quantum charge diffusion in underdamped Josephson junctions and superconducting nanowires
• Suppression of 2π phase-slip due to hidden zero modes in one dimensional topological superconductors
• Revisiting 2-pi phase slip suppression in topological Josephson junctions
• Voltage-Current curves for small Josephson junction arrays

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• 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