Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction

Abstract

We study junctions between superconductors mediated by the edge states of a quantum spin Hall insulator. We show that such junctions exhibit a fractional Josephson effect, in which the current phase relation has a 4π, rather than a 2πperiodicity. This effect is a consequence of the conservation of fermion parity - the number of electrons modulo 2 - in a superconducting junction, and is closely related to the Z_2 topological structure of the quantum spin Hall insulator. Inelastic processes, which violate the conservation of fermion parity, lead to telegraph noise in the equilibrium supercurrent. We predict that the low frequency noise due these processes diverges exponentially with temperature T as T -> 0. Possible experiments on HgCdTe quantum wells will be discussed.

4 pages, 2 figures

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• Dynamical transport measurement of the Luttinger parameter in helical edges states of 2D topological insulators
• Spin-Pairing Correlations and Spin Polarization of Majorana Bound States in Two-Dimensional Topological Insulator Systems
• Anomalous crossed Andreev reflection in mesoscopic superconducting ring hosting Majorana fermions
• Fractional Josephson effect in a quadruple quantum dot
• Signatures of Majorana Kramers pairs in superconductor-Luttinger liquid and superconductor-quantum dot-normal lead junctions
• Suppression of 2π phase-slip due to hidden zero modes in one dimensional topological superconductors
• Majorana fermions coupled to electromagnetic radiation
• Exact zero modes and decoherence in systems of interacting Majorana fermions
• Proposal for measuring the parity anomaly in a topological superconductor ring
• Current-phase relation and $h/e$-periodic critical current of a chiral Josephson contact between 1D Majorana modes
• Quantum phase slips in a resonant Josephson junction
• Josephson junctions of Weyl semimetal ${\text{WTe}}_2$ induced by spontaneous nucleation of $\text{PdTe}$ superconductor
• Effects of Gapless Bosonic Fluctuations on Majorana Fermions in Atomic Wire Coupled to a Molecular Reservoir
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
• Stability of entanglement-spectrum crossing in quench dynamics of one dimensional gapped free-fermion systems
• Localization-Driven Correlated States of Two Isolated Interacting Helical Edges
• Spontaneous breaking of time-reversal symmetry in topological superconductors
• Tomography of zero-energy end modes in topological superconducting wires
• Building a bigger Hilbert space for superconducting devices, one Bloch state at a time
• Electrical manipulation of Majorana fermions in an interdigitated superconductor-ferromagnet device
• Interplay between Rashba interaction and electromagnetic field in the edge states of a 2D topological insulator
• Fractional AC Josephson effect in a topological insulator proximitized by a self-formed superconductor
• Quantum phase transitions of the Majorana toric code in the presence of finite Cooper-pair tunneling
• Zero Bias Conductance Peak in Dirac Semimetal-Superconductor Devices
• Magnetism-induced massive Dirac spectra and topological defects in the surface state of Cr-doped Bi${}_2$Se${}_3$-bilayer topological insulators
• Majorana zero modes in twisted transition metal dichalcogenides homobilayers
• Identify the topological superconducting order in a multi-band quantum wire
• Bosonization for fermions and parafermions
• Majorana orthogonal transformation and Majorana zero modes in free fermionic systems
• Gate-defined Josephson weak-links in monolayer $\mathrm{WT}{\mathrm{e}}_2$
• Correlated parity measurements as a probe of non-abelian statistics in 1D superconducting wires
• Skyrmion spin texture in ferromagnetic semiconductor-superconductor heterostructures
• Josephson junction on one edge of a two dimensional topological insulator affected by magnetic impurity
• Effective model for Majorana modes in graphene
• Localized Andreev edge states in HgTe quantum wells
• Geometric dependence of Nb-Bi${}_2$Te${}_3$-Nb topological Josephson junction transport parameters
• Properties of the Majorana-state tunneling Josephson junction mediated by an interacting quantum dot
• Quantum transport in topological insulator hybrid structures -- A combination of topological insulator and superconductor
• Exciting odd frequency equal-spin-triplet correlations at metal-superconductor interfaces
• Period-doubling in the phase dynamics of a shunted HgTe quantum well Josephson junction
• Majorana states and devices in magnetic structures
• Topological aspects of $\pi$ phase winding junctions in superconducting wires
• The influence of the Majorana non-locality on the supercurrent
• Majorana signatures in charge transport through a topological superconducting double-island system
• Time-reversal-invariant topological superconductivity
• $8\pi$-periodic dissipationless ac Josephson effect on a quantum spin-Hall edge via a Quantum magnetic impurity
• Proposed Detection of the Topological Phase in Ring-Shaped Semiconductor-Superconductor Nanowires Using Coulomb Blockade Transport
• Majorana-induced DC Shapiro steps in topological Josephson junctions
• Enhanced Majorana bound states in magnetic chains on superconducting topological insulator edges
• Charge transfer statistics of transport through Majorana bound states
• Synthetic helical liquid in a quantum wire
• Platforms for the realization and characterization of Tomonaga-Luttinger liquids
• Leggett Modes in Dirac Semimetals
• Josephson junctions of 2D time-reversal invariant superconductors: signatures of the topological phase
• Fractional Shapiro steps without fractional Josephson effect
• Commuting-projector Hamiltonians for 2D topological insulators: edge physics and many-body invariants
• Reveal the non-local coherent nature from a dissipative Majorana teleportation
• Majorana lattices from the quantized Hall limit of a proximitized spin-orbit coupled electron gas
• Planar Josephson Hall effect in topological Josephson junctions
• Straining the Identity of Majorana Fermions
• Multiple Andreev reflections in s-wave superconductor-quantum dot- topological superconductor tunnel junctions and Majorana bound states
• Sea of Majorana fermions from pseudo-scalar superconducting order in three dimensional Dirac materials
• Generalized Thouless Pumps in 1+1-dimensional Interacting Fermionic Systems
• The invisible Majorana bound state at the helical edge
• Parity dependent Josephson current through a helical Luttinger liquid
• Giant spin splitting and $0-\pi$ Josephson transitions from the Edelstein effect in quantum spin-Hall insulators
• Conduction spectroscopy of a proximity induced superconducting topological insulator
• Demonstrating Entanglement by Testing Bell's Theorem in Majorana Wires
• Thermodynamics in topological Josephson junctions
• Moving Majorana bound states between distinct helical edges across a quantum point contact
• Bosonic edge states in gapped honeycomb lattices
• Detailed study of nonlinear cooling with two-terminal configurations of topological edge states
• Scattering in quantum wires and junctions of quantum wires with edge states of quantum spin Hall insulators
• Josephson radiation from nonlinear dynamics of Majorana zero modes
• Fractional Josephson effect in nonuniformly strained graphene
• Band structures and ${\mathbb{Z}}_2$ invariants of two-dimensional transition metal dichalcogenide monolayers from fully-relativistic Dirac-Kohn-Sham theory using Gaussian-type orbitals
• Quantum oscillations in 2D electron gases with spin-orbit and Zeeman interactions
• Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases
• Disorder-induced subgap states and Majorana zero-energy edge modes in two-dimensional topological insulator-superconductor hybrid structures
• Majorana bound states in topological insulators with hidden Dirac points
• Chiral current-phase relation of topological Josephson junctions: A signature of the $4\pi$-periodic Josephson effect
• Nonlocal Andreev reflection, fractional charge and current-phase relation in topological bilayer exciton condensate junctions
• Strong-coupling topological Josephson effect in quantum wires
• Soliton defects and topological $4\pi$-periodic superconductivity from an orbital magnetic field effect in edge Josephson junctions
• Josephson-Majorana cycle in topological single-electron hybrid transistors
• Parafermion stabilizer codes
• 2${\Phi }_0$-periodic magnetic interference in ballistic graphene Josephson junctions
• Edge absorption and pure spin current in 2D topological insulator in the Volkov-Pankratov model
• Waiting time distributions in Quantum spin hall based heterostructures
• Revisiting 2-pi phase slip suppression in topological Josephson junctions
• AC Josephson effect in a gate-tunable Cd${}_3$As${}_2$ nanowire superconducting weak link
• Bulk Pumping in 2D Topological Phases
• Influences of electron-phonon interaction on quantum transport through one quantum-dot system with side-coupled Majorana zero mode
• Signature of Anomalous Andreev bound states in magnetic Josephson junction of noncentrosymmetric superconductor on a topological insulator
• Anomalous photon-assisted tunneling in periodically driven Majorana nanowires and BCS Charge Measurement
• Supercurrent vortices and Majorana zero modes induced by an inplane Zeeman field on the surface of a three-dimensional topological insulator
• Minimal circuit for a flux-controlled Majorana qubit in a quantum spin-Hall insulator
• Detecting Majorana fermions by use of superconductor-quantum Hall liquid junctions
• Nonlocality of Majorana bound states revealed by electron waiting times in a topological Andreev interferometer
• Topological multiband s-wave superconductivity in coupled multifold fermions
• Surface-dependent Majorana vortex phases in topological crystalline insulators
• Josephson dynamics at high transmissions: Perturbation theory
• Insulating regime of an underdamped current-biased Josephson junction supporting ${\mathbb{Z}}_3$ and ${\mathbb{Z}}_4$ parafermions
• Quasiparticle states and quantum interference induce by magnetic impurities on a two-dimensional topological superconductor
• Nonequilibrium Andreev bound states population in short superconducting junctions coupled to a resonator
• Fraunhofer pattern in the presence of Majorana zero modes
• Determination of Cooper pairs and Majorana fermions currents ratio in DC-SQUID with topologically nontrivial barriers
• Charge quantization and detector resolution
• Theory of topological spin Josephson junctions
• Voltage-tunable Majorana bound states in time-reversal symmetric bilayer quantum spin Hall hybrid systems
• Control of Andreev bound state population and related charge-imbalance effect
• Protected gap closing in Josephson junctions constructed on Bi${}_2$Te${}_3$ surface
• Controlling Majorana hybridization in magnetic chain-superconductor systems
• Fano resonances can provide two criteria to distinguish Majorana bound states from other candidates in experiments
• Critical current for an insulating regime of an underdamped current-biased topological Josephson junction
• Transport in topological insulator nanowires
• Topological charge, spin and heat transistor
• Josephson current between two $p$-wave superconducting nanowires in the presence of Rashba spin-orbit interaction and Zeeman magnetic fields
• Current Flow in Topological Insulator Josephson Junctions due to Imperfections
• Interplay between Coulomb blockade and Josephson effect in a topological superconductor-quantum dot device
• Josephson current signature of Floquet Majorana and topological accidental zero modes in altermagnet heterostructures
• Majorana-magnon interactions in topological Shiba chains
• Flux sensitivity of quantum spin Hall rings
• Effect of Magnetic Field and Rashba Spin-Orbit Interaction on the Josephson Tunneling between Superconducting Nanowires
• Fermion-parity switches of the ground state of Majorana billiards
• Symmetry analysis of transport properties in helical superconductor junctions
• Topology protection-unprotection transition: an example from multi-terminal superconducting nanostructures
• Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers II: Zero-field topological superconductivity
• Identifying Majorana bound states at quantum spin Hall edges using a metallic probe
• Electromotive force in driven topological quantum circuits
• Phonon-induced Majorana Qubit Relaxation in Tunnel-Coupled Two-Island Topological Superconductors
• Unusual Superconducting Proximity Effect in Magnetically Doped Topological Josephson Junctions
• Quasiparticle poisoning in trivial and topological Josephson junctions
• Current--phase relation in a topological Josephson junction: Andreev bands vs. scattering states
• Missing odd-order Shapiro steps do not uniquely indicate fractional Josephson effect
• Majorana fermions in semiconductor nanostructures with two wires connected through ring
• Edge supercurrent in Josephson junctions based on topological materials
• Topological Josephson Junctions in the Integer Quantum Hall Regime
• Electrically controlled crossover between $2\pi$- and $4\pi$-Josephson effects through topologically-confined channels in silicene
• Quantum computing through electron propagation in the edge states of quantum spin Hall systems
• All-electrical spectroscopy of topological phases in semiconductor-superconductor heterostructures
• Topological Josephson Bifurcation Amplifier: Semiclassical theory
• Exact analytical solution of a time-reversal-invariant topological superconducting wire
• Superconducting quantum spin-Hall systems with giant orbital g-factors
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor
• Detection of Majorana zero modes bound to Josephson vortices in planar superconductor-topological insulator-superconductor junctions
• Time reversal invariant gapped boundaries of the double semion state
• Proximity-reduced range of internal phase differences in double Josephson junctions with closely spaced interfaces
• Higher-order topological superconductor phases in a multilayer system
• Quantum Phase Transitions in Proximitized Josephson Junctions
• Probing Majorana bound states via a pn-junction containing a quantum dot
• Tuning Majorana zero modes with temperature in $\pi$-phase Josephson junctions
• Gate Tunable Supercurrent in Josephson Junctions Based on Bi2Te3 Topological Insulator Thin Films
• 4$\pi$ and 8$\pi$ dual Josephson effects induced by symmetry defects
• Lifshitz transitions and Weyl semimetals from a topological superconductor with supercurrent flow
• Majorana Thermoelectrics and Refrigeration
• Backscattering off a driven Rashba impurity at the helical edge
• Quantum transport theory of hybrid superconducting systems
• Exceptional Andreev spectrum and supercurrent in p-wave non-Hermitian Josephson junctions
• Topologically Induced Fermion Parity Flips in Superconductor Vortices
• Interaction effects in superconductor/quantum spin Hall devices: universal transport signatures and fractional Coulomb blockade
• Microwave signatures of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_4$ fractional Josephson effects
• Josephson radiation in a superconductor-quantum dot-superconductor junction
• Atomistic modeling of a superconductor-transition-metal dichalcogenide-superconductor Josephson junction
• All-electrically reading out and initializing topological qubits with quantum dots
• Quantum Hall valley Ferromagnets as a platform for topologically protected quantum memory
• Superconductor/normal-metal/superconductor junction of topological superconductors revisited: Fractional Josephson current, fermion parity, and oscillating wavefunctions
• Topological properties of finite-size heterostructures of magnetic topological insulators and superconductors
• Topological superconductivity in proximity to type-II superconductors
• Hanbury Brown and Twiss Correlations of Cooper Pairs in Helical Liquids
• Strong effects of weak ac driving in short superconducting junctions
• In the Pursuit of Majorana Modes in Iron-based High-$T_c$ Superconductors
• Correlation and current anomalies in helical quantum dots
• Physics of the Majorana-superconducting qubit hybrids
• Fingerprints of Majorana bound states in quantum-rings
• Universal Current Correlations Induced by the Majorana and Fermionic Andreev Bound States
• Majorana zero modes in a quantum wire platform without Rashba spin-orbit coupling
• AC anomalous Hall effect in topological insulator Josephson junctions
• From Majorana fermions to topological quantum computation in semiconductor/superconductor heterostructures
• Robustness of Topological Order in Semiconductor-Superconductor Nanowires in the Coulomb Blockade Regime
• Assessing bound states in a one-dimensional topological superconductor: Majorana versus Tamm
• Nonequilibrium Spectroscopy of Topological Edge Liquids
• Chirality-selective proximity effect between chiral $p$-wave superconductors and quantum Hall insulators
• Quantum spin Hall insulator in proximity with a superconductor: Transition to the Fulde-Ferrell-Larkin-Ovchinnikov state driven by a Zeeman field
• Chiral Edge Currents in a Holographic Josephson Junction
• A Green's function approach to Topological Insulator junctions with magnetic and superconducting regions
• Fractionalization of Majorana-Ising-type quasiparticles
• Many-body Majorana-like zero modes without gauge symmetry breaking
• Phase-dependent charge and heat current in thermally biased short Josephson junctions formed at helical edge states
• Spin-Exchange Induced Spillover on Poor Man's Majoranas in Minimal Kitaev Chains
• Superconducting spin properties of Majorana nanowires and the associated superconducting anomalous Hall effect
• Vortex detection and quantum transport in mesoscopic graphene Josephson junction arrays
• Representation-protected topology of spin-singlet $s$-wave superconductors
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• Twofold twist defect chains at criticality
• Phase-tunable multiple Andreev reflections in a quantum spin Hall strip
• Current-phase relation of a short multi-mode Bi2Se3 topological insulator nanoribbon Josephson junction with ballistic transport modes
• Integration of graphene-based superconducting quantum circuits in 3D cavity
• A Study of Topological Quantum Phase Transition and Majorana Localization Length for the Interacting Helical Liquid System
• Ever-present Majorana bound state in a generic one-dimensional superconductor with odd number of Fermi surfaces
• Quantum critical points in tunneling junction of topological superconductor and topological insulator
• Embedded Majorana Islands
• Absence of "fractional ac Josephson effect" in superconducting junctions
• Parity-protected superconducting qubit based on topological insulators
• Bulk transport through superconducting hybrid structures in HgTe quantum wells
• Time-dependent driving and topological protection in the fractional Josephson effect
• Identifying biases of the Majorana scattering invariant
• Shuttling Majorana zero modes in disordered and noisy topological superconductors
• Majorana bound state parity exchanges in planar Josephson junctions
• Majorana modes in helical altermagnet without net magnetism and spin-orbit coupling
• Boundary-induced Majorana coupling in a planar topological Josephson junction
• Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator
• Bulk-boundary correspondence in Josephson Junctions
• Unified scattering approach to Josephson current and thermal noise in BCS and topological superconducting junctions
• Non-Abelian Evolution of a Majorana Train in a Single Josephson Junction
• Disordered Quantum Transport in Quantum Anomalous Hall Insulator-Superconductor Junctions
• Random-gate-voltage induced Al'tshuler-Aronov-Spivak effect in topological edge states
• Zero-energy quasiparticles in an interacting nanowire containing a topological Josephson junction
• Repulsive Casimir force from a Majorana zero-mode
• Majorana Zero Modes and Topological Nature in Bi2Ta3S6-family Superconductors
• Detecting Majorana modes through Josephson junction ring-quantum dot hybrid architectures
• A simple electronic ladder model harboring ${\mathbb{Z}}_4$ parafermions
• Robust Majorana bound state in pseudo-spin domain wall of 2-D topological insulator
• Josephson radiation patterns in underdamped topological Josephson junctions
• Cross correlation mediated by distant Majorana zero modes with no overlap
• Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology
• Helical spin texture and interference of Majorana bound states in one-dimensional topological superconductor
• Interedge backscattering in time-reversal symmetric quantum spin Hall Josephson junctions
• Signatures of Parafermion Zero Modes in Fractional Quantum Hall-Superconductor Heterostructures
• Nonreciprocal Equilibrium Josephson Effect of Arbitrary Periodicity from Poor Man's Majorana Zero Modes
• Anomalous flux periodicity in proximitised quantum spin Hall constrictions
• Majorana fermion induced power-law scaling in the violations of the Wiedemann-Franz law
• Manifestation of edge-bulk incompatibility in fractional quantum Hall platform
• Interplay between evanescent scattering modes and finite dispersion in superconducting junctions
• Origin of Robust ${\mathbb{Z}}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion
• Confinement-induced Majorana modes in a nodal topological superconductor
• Control of Majorana Edge Modes by a g-factor Engineered Nanowire Spin Transistor
• Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors
• Ubiquitous missing first Shapiro step in Al-InSb nanosheet Josephson junctions
• Pairing around a Single Dirac Point: A Unifying View of Kohn-Luttinger Superconductivity in Chern Bands, Quarter Metals, and Topological Surface States
• Auto- and cross-correlations in the spinful topological Kondo model
• Unveiling Topological Hinge States in the Higher-Order Topological Insulator WTe${}_2$ Based on the Fractional Josephson Effect
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• Majorana bound states with chiral magnetic textures
• Tunable effective length of fractional Josephson junctions
• Boundary conditions for the order parameter and the proximity influenced internal phase differences in double superconducting junctions
• Electron density and compressibility in the Kitaev model with a spatially modulated Phase in the superconducting pairing
• Fluctuation response of a minimal Kitaev chain in nonequilibrium states
• Highly skewed current-phase relation in superconductor-topological insulator-superconductor Josephson junctions
• Pre-Patterned Superconducting Contacts for Clean Superconductor-Topological Material Interfaces Enabling Long-Range Josephson Coupling
• Limits of Thermal Conductance Quantization in Chiral Topological Josephson Junctions
• Giant and robust Josephson diode effect in multiband topological nanowires
• Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity
• Electrical transport through a quantum dot side-coupled to a topological superconductor
• Field-free Superconducting Diode Effect and Topological Fulde-Ferrell Superconductivity in Altermagnetic Shiba Chains
• Rashba spin-orbit coupling and artificially engineered topological superconductors
• Persistent ferromagnetism and topological phase transition at the interface of a superconductor and a topological insulator
• Edge dependence of the Josephson current in the quantum Hall regime
• Majorana Conductances in Three-Terminal Transports
• Phase-dependent supercurrent and microwave dissipation of HgTe quantum well Josephson junctions
• Topological superconductivity and fractional Josephson effect in quasi-one dimensional wires on a plane
• Fractional spin Josephson effect in topological spin superconductors
• Buried Dirac points in quantum spin Hall insulators: Implications for Majorana Kramers pair-based quantum computing
• Identification of odd-frequency superconducting pairing in Josephson junctions
• Nonlocal signatures of hybridization between quantum dot and Andreev bound states
• Parity flipping mediated by a quantum dot in Majorana Josephson junctions