Chiral current-phase relation of topological Josephson junctions: A signature of the $4\pi$-periodic Josephson effect

Abstract

The $4\pi$-periodic Josephson effect is an indicator of Majorana zero modes and a ground-state degeneracy which are central to topological quantum computation. However, the observability of a $4\pi$-periodic Josephson current-phase relation (CPR) is hindered by the necessity to fix the fermionic parity. As an alternative to a $4\pi$-periodic CPR, this paper proposes a chiral CPR for the $4\pi$-periodic Josephson effect. This is a CPR of the form $J(\varphi )\propto C|\sin (\varphi /2)|$, describing a unidirectional supercurrent with the chirality $C=\pm 1$. Its non-analytic dependence on the Josephson phase difference $\varphi$ translates into the $4\pi$-periodic CPR $J(\varphi )\propto \sin (\varphi /2)$. The proposal requires a spin-polarized topological Josephson junction which is modeled here as a short link between spin-split superconducting channels at the edge of a two-dimensional topological insulator. In this case, $C$ coincides with the Chern number of the occupied spin band of the topological insulator. The paper details three scenarios of achieving a chiral CPR: By only Zeeman-like splitting, by Zeeman splitting combined with bias currents, and by an external out-of-plane magnetic field.

arXiv comment8 pages, 4 figures, published version

References in corpus (41)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• 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
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Search for Majorana fermions in superconductors
• Topological superconductors: a review
• Majorana fermions in a tunable semiconductor device
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Majorana Zero Modes and Topological Quantum Computation
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Chiral Topological Superconductor From the Quantum Hall State
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Manipulation of Majorana fermion, Andreev reflection and Josephson current on topological insulators
• $4\pi$-periodic Josephson supercurrent in HgTe-based topological Josephson junctions
• AC Josephson effect in finite-length nanowire junctions with Majorana modes
• Anomalous Josephson Current in Junctions with Spin-Polarizing Quantum Point Contacts
• Anomalous Josephson current through a spin-orbit coupled quantum dot
• Dynamical detection of Majorana fermions in current-biased nanowires
• Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect
• Topological Josephson ${\varphi }_0$-junctions
• Observation of the 4$\pi$-periodic Josephson effect in indium arsenide nanowires
• Non-equilibrium Josephson effect through helical edge states
• Majorana splitting from critical currents in Josephson junctions
• Phenomenology and Dynamics of Majorana Josephson Junction
• Manipulating Majorana fermions using supercurrents
• Spin-helical transport in normal and superconducting topological insulators
• Fractional ac Josephson effect in unconventional superconductors
• Ac Josephson Effect in Topological Josephson Junctions
• Anomalous low-temperature enhancement of supercurrent in topological-insulator nanoribbon Josephson junctions: evidence for low-energy Andreev bound states
• Parity anomaly and spin transmutation in quantum spin Hall Josephson junctions
• Magnetoelectric Andreev effect due to proximity-induced non-unitary triplet superconductivity in helical metals
• Magnetic field influence on the proximity effect in semiconductor - superconductor hybrid structures and their thermal conductance
• Andreev magnetotransport in low-dimensional proximity structures: Spin-dependent conductance enhancement
• Nonmetallic thermal transport in low-dimensional proximity structures with partially preserved time-reversal symmetry in a magnetic field
• Spectral Properties and Quantum Phase Transitions in Superconducting Junctions with a Ferromagnetic Link
• Giant spin splitting and $0-\pi$ Josephson transitions from the Edelstein effect in quantum spin-Hall insulators
• Soliton defects and topological $4\pi$-periodic superconductivity from an orbital magnetic field effect in edge Josephson junctions
• Probing the magnetoelectric effect in noncentrosymmetric superconductors by equal-spin Andreev tunneling

Cited by in corpus (7)

• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Field-Effect Josephson Diode via Asymmetric Spin-Momentum-Locking States
• Zero-frequency supercurrent susceptibility signatures of trivial and topological zero-energy states in nanowire junctions
• Superconducting Diode Effect in Quantum Spin Hall Insulator-based Josephson Junctions
• Thermodynamics in topological Josephson junctions
• Planar Josephson Hall effect in topological Josephson junctions
• Current-phase relation of a short multi-mode Bi2Se3 topological insulator nanoribbon Josephson junction with ballistic transport modes