Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect

Abstract

We study the Josephson junction mediated by the quantum spin Hall edge states and show that electron-electron interactions lead to a dissipationless fractional Josephson effect in the presence of time-reversal symmetry. Surprisingly, the periodicity is $8\pi$, corresponding to a Josephson frequency $eV/2\hslash$. We estimate the magnitude of interaction induced many-body level splitting responsible for this effect and argue that it can be measured using tunneling spectroscopy. For strong interactions we show that the Josephson effect is associated with the weak tunneling of charge $e/2$ quasiparticles between the superconductors. Our theory describes a fourfold ground state degeneracy that is similar to that of coupled "fractional" Majorana modes, but is protected by time reversal symmetry.

5 pages and 3 figures

References in corpus (13)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Phase controlled superconducting proximity effect probed by tunneling spectroscopy
• Fractional topological superconductors with fractionalized Majorana fermions
• Transition from fractional to Majorana fermions in Rashba nanowires

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