Current-phase relation for Josephson effect through helical metal

Abstract

Josephson junctions fabricated on the surface of three-dimensional topological insulators (TI) show a few unusual properties distinct from conventional Josephson junctions. In these devices, the Josephson coupling and the supercurrent are mediated by helical metal, the two-dimensional surface of the TI. A line junction of this kind is known to support Andreev bound states at zero energy for phase bias π, and consequently the so-called fractional ac Josephson effect. Motivated by recent experiments on TI-based Josephson junctions, here we describe a convenient algorithm to compute the bound state spectrum and the current-phase relation for junctions with finite length and width. We present analytical results for the bound state spectrum, and discuss the dependence of the current-phase relation on the length and width of the junction, the chemical potential of the helical metal, and temperature. A thorough understanding of the current-phase relation may help in designing topological superconducting qubits and manipulating Majorana fermions.

References in corpus (26)

• Topological Insulators
• Topological insulators and superconductors
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Quantum state engineering with Josephson-junction devices
• Andreev reflection and Klein tunneling in graphene
• Specular Andreev reflection in graphene
• Band structure engineering in (Bi1-xSbx)2Te3 ternary topological insulators
• Manipulation of Majorana fermion, Andreev reflection and Josephson current on topological insulators
• Bulk Band Gap and Surface State Conduction Observed in Voltage-Tuned Crystals of the Topological Insulator Bi${}_2$Se${}_3$
• Ambipolar Field Effect in Topological Insulator Nanoplates of (BixSb1-x)2Te3
• Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3
• Unconventional Josephson Effect in Hybrid Superconductor-Topological Insulator Devices
• Josephson supercurrent through a topological insulator surface state
• Gate-tuned normal and superconducting transport at the surface of a topological insulator
• Ultra-low carrier concentration and surface dominant transport in Sb-doped Bi2Se3 topological insulator nanoribbons
• Proximity effect at the superconductor - topological insulator interface
• Observation of the superconducting proximity effect and possible evidence for Pearl vortices in a candidate topological insulator
• Interplay between Superconductivity and Ferromagnetism on a Topological Insulator
• Strong Superconducting Proximity Effect in Pb-Bi2Te3 Hybrid Structures
• Topological quantum buses: coherent quantum information transfer between topological and conventional qubits
• Interface Between Topological and Superconducting Qubits
• Anomalous Josephson current via Majorana bound states in topological insulators
• Josephson and proximity effects on the surface of a topological insulator
• Microscopic simulation of superconductor-topological insulator proximity structures
• Mott scattering at the interface between a metal and a topological insulator
• Nearly flat Andreev bound states in superconductor-topological insulator hybrid structures

Cited by in corpus (24)

• $4\pi$-periodic Josephson supercurrent in HgTe-based topological Josephson junctions
• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Non-sinusoidal current-phase relationship in Josephson junctions from the 3D topological insulator HgTe
• Evidence for an anomalous current phase relation in topological insulator Josephson junctions
• Odd-frequency superconducting pairing in one-dimensional systems
• Spin-helical transport in normal and superconducting topological insulators
• Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism
• Superconducting proximity effect in three-dimensional topological insulators in the presence of a magnetic field
• Helical Andreev bound states and superconducting Klein tunneling in topological insulator Josephson junctions
• Andreev bound states and current-phase relations in three-dimensional topological insulators
• π and 4π Josephson Effects Mediated by a Dirac Semimetal
• High efficiency thermal switch based on topological Josephson junctions
• Anomalous low-temperature enhancement of supercurrent in topological-insulator nanoribbon Josephson junctions: evidence for low-energy Andreev bound states
• Signatures of a 4$\pi$-periodic supercurrent in the voltage response of capacitively shunted topological Josephson junctions
• Tunable hybridization of Majorana bound states at the quantum spin Hall edge
• Signature of a topological phase transition in the Josephson supercurrent through a topological insulator
• Josephson effect in a Weyl SNS junction
• Josephson current signatures of the Majorana flat bands on the surface of time-reversal-invariant Weyl and Dirac semimetals
• Majorana-Josephson Interferometer
• Microwave studies of the fractional Josephson effect in HgTe-based Josephson junctions
• Effect of impurities on the Josephson current through helical metals: Exploiting a neutrino paradigm
• Signature of Anomalous Andreev bound states in magnetic Josephson junction of noncentrosymmetric superconductor on a topological insulator
• Gate Tunable Supercurrent in Josephson Junctions Based on Bi2Te3 Topological Insulator Thin Films
• Localization and Topology in Noncentrosymmetric Superconductors with Disorder