Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors

Abstract

We study the joint dynamics of the phase bias $\varphi$ and the propagating Majorana fermions of the edge modes in Josephson junctions containing 2D time-reversal invariant topological superconductors (TRITOPS). We consider TRITOPS-TRITOPS junctions, as well as junctions between topological and non-topological superconductors (TRITOPS-S). Both types of junctions are described by effective Dirac Hamiltonians with a $\varphi$-dependent mass. We analyze the effect of the phase fluctuations in the junction, as well as solitonic solutions of $\varphi$ generated by fluxons trapped in the junction. We show that these solitons generate a spatial-dependent mass with a sign change akin to the Jackiw-Rebbi model. This enables the formation of zero-energy fermionic states localized at the fluxon. For the TRITOPS-TRITOPS junction these consist of a Kramers pair of Majorana modes, while for the TRITOPS-S one, there is a single Majorana fermion. The localized bound states hybridize in soliton-antisoliton configurations. Depending on the occupation state, these modes generate an effective attraction or repulsion in the dynamics of the soliton-antisoliton collision.

References in corpus (64)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• 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
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Topological superconductors: a review
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Exponential Protection of Zero Modes in Majorana Islands
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Zoo of quantum-topological phases of matter
• Odd-Parity Topological Superconductors: Theory and Application to Cu${}_x$Bi${}_2$Se${}_3$
• Observation of topological superconductivity on the surface of an iron-based superconductor
• Topological Superconductivity and Superfluidity
• Evidence of topological superconductivity in planar Josephson junctions
• Topological superconductivity in a van der Waals heterostructure
• Fractional ac Josephson effect in p- and d-wave superconductors
• End states and subgap structure in proximity-coupled chains of magnetic adatoms
• Topological Superconductivity in a Phase-Controlled Josephson Junction
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Time Reversal Invariant Topological Superconductivity and Majorana Kramers Pairs
• Topological Superconductivity in a Planar Josephson Junction
• Signature of Dispersing 1D Majorana Channels in an Iron-based Superconductor
• Anomalous Andreev bound state in non-centrosymmetric superconductors
• Emergent Supersymmetry from Strongly Interacting Majorana Zero Modes
• Inducing time reversal invariant topological superconductivity and fermion parity pumping in quantum wires
• Majorana Kramers Doublets in $d_{x^2-y^2}$-wave Superconductors with Rashba Spin-Orbit Coupling
• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Majorana bound states and non-local spin correlations in a quantum wire on an unconventional superconductor
• Topological superconductivity and unconventional pairing in oxide interfaces
• Majorana modes in time-reversal invariant s-wave topological superconductors
• Time-Reversal Invariant Topological Superconductivity Induced by Repulsive Interactions in Quantum Wires
• Observing Majorana bound states of Josephson vortices in topological superconductors
• Proximity-induced Josephson $\pi$-Junctions in Topological Insulators
• Superconductivity on the surface of topological insulators and in two-dimensional noncentrosymmetric materials
• Fractional Josephson Vortices and Braiding of Majorana Zero Modes in Planar Superconductor-Semiconductor Heterostructures
• Benefits of weak disorder in one dimensional topological superconductors
• Theory of time reversal topological superconductivity in double Rashba wires -- symmetries of Cooper pair and Andreev bound states
• Parity-controlled $2\pi$ Josephson effect mediated by Majorana Kramers pairs
• Time-reversal anomaly and Josephson effect in time-reversal invariant topological superconductors
• Topological superconductivity in planar Josephson junctions: Narrowing down to the nanowire limit
• Topological Properties of Time Reversal Symmetric Kitaev Chain and Applications to Organic Superconductors
• Detection of Majorana Kramers pairs using a quantum point contact
• Fractional spin and Josephson effect in time-reversal-invariant topological superconductors
• DIII Topological Superconductivity with Emergent Time-Reversal Symmetry
• Interaction-driven topological superconductivity in one dimension
• Highly tunable time-reversal-invariant topological superconductivity in topological insulator thin films
• Signatures of time-reversal-invariant topological superconductivity in the Josephson effect
• Entangled end states with fractionalized spin projection in a time-reversal-invariant topological superconducting wire
• Impact of topology on the impurity effects in extended $s$-wave superconductors with spin-orbit coupling
• Catalogue of Andreev spectra and Josephson effects in structures with time-reversal-invariant topological superconductor wires
• Proximity induced time-reversal topological superconductivity in Bi2Se3 films without phase tuning
• Friedel oscillations and Majorana zero modes in inhomogeneous superconductors
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
• Topological superconducting phases and Josephson effect in curved time-reversal-invariant superconductors
• Josephson junctions of 2D time-reversal invariant superconductors: signatures of the topological phase
• Time-Reversal Invariant Topological Superconductivity in Planar Josephson Bijunction
• Spontaneous Josephson $\pi$ Junctions with Topological Superconductors
• Transport features of a topological superconducting nanowire with a quantum dot: conductance and noise
• Magnetization Dynamics and Peierls Instability in Topological Josephson Structures
• Effect of interatomic repulsion on Majorana zero modes in a coupled quantum-dot-superconducting-nanowire hybrid system

Cited by in corpus (1)

• Limits of Thermal Conductance Quantization in Chiral Topological Josephson Junctions