Fractional spin and Josephson effect in time-reversal-invariant topological superconductors

Abstract

Time reversal invariant topological superconducting (TRITOPS) wires are known to host a fractional spin hbar/4 at their ends. We investigate how this fractional spin affects the Josephson current in a TRITOPS-quantum dot-TRITOPS Josephson junction, describing the wire in a model which can be tuned between a topological and a nontopological phase. We compute the equilibrium Josephson current of the full model by continuous-time Monte Carlo simulations and interpret the results within an effective low-energy theory. We show that in the topological phase, the 0-to-pi transition is quenched via formation of a spin singlet from the quantum dot spin and the fractional spins associated with the two adjacent topological superconductors.

4+1 pages, 3 figures, supplemental material (published version)

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• Boundary Green's function approach for spinful single-channel and multichannel Majorana nanowires
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• Practical Guide to Quantum Phase Transitions in Quantum-Dot-Based Tunable Josephson Junctions
• Entangled end states with fractionalized spin projection in a time-reversal-invariant topological superconducting wire
• Absence of supercurrent sign reversal in a topological junction with a quantum dot
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• 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
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• Topological superconducting phases and Josephson effect in curved time-reversal-invariant superconductors
• Survival of the fractional Josephson effect in time-reversal-invariant topological 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
• Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems
• Topological Kondo effect with spinful Majorana fermions
• Exact analytical solution of a time-reversal-invariant topological superconducting wire
• Enhancement of the Kondo effect in a quantum dot formed in a full-shell nanowire
• Effect of interatomic repulsion on Majorana zero modes in a coupled quantum-dot-superconducting-nanowire hybrid system
• Fusion Rules of Majorana-Kramer-Pairs in Time-Reversal-Invariant Topological Superconductors
• Designing ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ topological orders in networks of Majorana bound states
• Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors
• Fractional spin Josephson effect in topological spin superconductors