Beyond the standard model of topological Josephson junctions: From crystalline anisotropy to finite-size and diode effects

Abstract

A planar Josephson junction is a versatile platform to realize topological superconductivity over a large parameter space and host Majorana bound states. With a change in Zeeman field, this system undergoes a transition from trivial to topological superconductivity accompanied by a jump in the superconducting phase difference between the two superconductors. A standard model of these Josephson junctions, which can be fabricated to have a nearly perfect interfacial transparency, predicts a simple universal behavior. In that model, at the same value of Zeeman field for the topological transition, there is a $\pi$ phase jump and a minimum in the critical superconducting current, while applying a controllable phase difference yields a diamond-shaped topological region as a function of that phase difference and a Zeeman field. In contrast, even for a perfect interfacial transparency, we find a much richer and nonuniversal behavior as the width of the superconductor is varied or the Dresselhaus spin-orbit coupling is considered. The Zeeman field for the phase jump, not necessarily $\pi$, is different from the value for the minimum critical current, while there is a strong deviation from the diamond-like topological region. These Josephson junctions show a striking example of a nonreciprocal transport and superconducting diode effect, revealing the importance of our findings not only for topological superconductivity and fault-tolerant quantum computing, but also for superconducting spintronics.

arXiv commentInvited to APL Special Topic Issue: "Josephson Junctions and Related Proximity Effects: From Basic Science to Emerging Applications in Advanced Technologies", accepted version

References in corpus (63)

• Spintronics: Fundamentals and applications
• Fault-tolerant quantum computation by anyons
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Kwant: a software package for quantum transport
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Superconducting Spintronics
• Introduction to topological superconductivity and Majorana fermions
• Spin-polarized supercurrents for spintronics: a review of current progress
• Milestones toward Majorana-based quantum computing
• A Josephson junction supercurrent diode
• Evidence of topological superconductivity in planar Josephson junctions
• Zero-bias anomaly in a nanowire quantum dot coupled to superconductors
• Topological Superconductivity in a Phase-Controlled Josephson Junction
• Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks
• Classification of Topological Insulators and Superconductors
• Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors
• Topological invariants for spin-orbit coupled superconductor nanowires
• Topological Superconductivity in a Planar Josephson Junction
• Anomalous Josephson effect induced by spin-orbit interaction and Zeeman effect in semiconductor nanowires
• Two-dimensional platform for networks of Majorana bound states
• Ubiquitous Superconducting Diode Effect in Superconductor Thin Films
• Non-Majorana states yield nearly quantized conductance in superconductor-semiconductor nanowire devices
• Disorder-induced zero-bias peaks in Majorana nanowires
• Inducing time reversal invariant topological superconductivity and fermion parity pumping in quantum wires
• Ubiquitous non-Majorana Zero-Bias Conductance Peaks in Nanowire Devices
• Transparent Semiconductor-Superconductor Interface and Induced Gap in an Epitaxial Heterostructure Josephson Junction
• Phase signature of topological transition in Josephson Junctions
• Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions
• Time reversal non-invariant non-Abelian topological order in non-centrosymmetric superconductors
• Majorana nanowires for topological quantum computation
• Reversible control of spin-polarised supercurrents in ferromagnetic Josephson junctions
• Relating Andreev Bound States and Supercurrents in Hybrid Josephson Junctions
• The multi-terminal Josephson effect
• Cubic spin-orbit coupling and anomalous Josephson effect in planar junctions
• Wireless Majorana Bound States: From Magnetic Tunability to Braiding
• Fusion of Majorana Bound States with Mini-Gate Control in Two-Dimensional Systems
• Hard superconducting gap in germanium
• Majorana bound states in semiconducting nanostructures
• Fractional Josephson Vortices and Braiding of Majorana Zero Modes in Planar Superconductor-Semiconductor Heterostructures
• Phase Control of Majorana Bound States in a Topological X Junction
• Signatures of a topological phase transition in a planar Josephson junction
• Tuning Topological Superconductivity in Phase-Controlled Josephson Junctions with Rashba and Dresselhaus Spin-Orbit Coupling
• Topological superconductivity in planar Josephson junctions: Narrowing down to the nanowire limit
• Tunable Magnetic Textures: From Majorana Bound States to Braiding
• Superconducting Diode Effect Sign Change in Epitaxial Al-InAs Josepshon Junctions
• Anisotropic topological superconductivity in Josephson junctions
• Synthetic Weyl Points and Chiral Anomaly in Majorana Devices with Nonstandard Andreev-Bound-State Spectra
• Disorder in Andreev reflection of a quantum Hall edge
• Full proximity treatment of topological superconductors in Josephson-junction architectures
• Control of Andreev bound states using superconducting phase texture
• Topological superconductivity in Rashba semiconductors without a Zeeman field
• Majorana bound states in hybrid 2D Josephson junctions with ferromagnetic insulators
• Planar Josephson junctions in germanium: Effect of cubic spin-orbit interaction
• Crystalline Anisotropic Topological Superconductivity in Planar Josephson Junctions
• Selective-Area-Grown PbTe-Pb Planar Josephson Junctions for Quantum Devices
• Phenomenological Theory of the Supercurrent Diode Effect: The Lifshitz Invariant

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• Superconducting diode efficiency from singlet-triplet mixing in disordered systems
• Microwave Signatures of Topological Superconductivity in Planar Josephson Junctions
• Disorder effects in planar semiconductor-superconductor structures: Majorana wires versus Josephson junctions
• Microwave Andreev bound state spectroscopy in a semiconductor-based Planar Josephson junction
• Planar Josephson junction devices with narrow superconducting strips: Topological properties and optimization
• Majorana edge and end states in planar Josephson junctions