Josephson-Current Signatures of Unpaired Floquet Majorana Bound States

Abstract

We theoretically study the transport signatures of unpaired Floquet Majorana bound states in the Josephson current of weakly linked, periodically driven topological superconductors. We obtain the occupation of the Floquet Majorana modes in the presence of weak coupling to thermal leads analytically, and show that, similar to static superconductors, the Josephson current involving Floquet Majorana bound states is also $4\pi$-periodic in the phase difference across the junction, and also depends linearly on the coupling between superconductors. Moreover, unlike the static case, the amplitude of the Josephson current can be tuned by setting the unbiased chemical potential of the driven superconductors at multiple harmonics of the drive frequency. As a result, we uncover a Josephson Floquet sum rule for driven superconductors. We confirm our analytical expressions for Josephson current, the occupation of Floquet bands, and a perturbative analysis of the quasienergies with numerically exact results.

arXiv comment13 pages including appendices

References in corpus (79)

• Topological Insulators
• Topological insulators and superconductors
• 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
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Photonic Floquet Topological Insulators
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Experimental realisation of the topological Haldane model
• Search for Majorana fermions in superconductors
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Photovoltaic Hall effect in graphene
• Observation of Floquet-Bloch states on the surface of a topological insulator
• Topological characterization of periodically-driven quantum systems
• Atomic quantum gases in periodically driven optical lattices
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• Majorana Fermion Induced Resonant Andreev Reflection
• Light-induced anomalous Hall effect in graphene
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Introduction to topological superconductivity and Majorana fermions
• Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Tunneling characteristic of a chain of Majorana bound states
• Floquet topological insulators
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Zero-bias peaks in spin-orbit coupled superconducting wires with and without Majorana end-states
• Majorana Fermions in Semiconductor Nanowires: Fundamentals, Modeling, and Experiment
• Unconventional superconductivity on a topological insulator
• Floquet-Bloch theory and topology in periodically driven lattices
• Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon
• Fractional ac Josephson effect in p- and d-wave superconductors
• Observation of Topological Band Gap Solitons
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Realization of an anomalous Floquet topological system with ultracold atoms
• Floquet chiral edge states in graphene
• Topological singularities and the general classification of Floquet-Bloch systems
• Quantized conductance at the Majorana phase transition in a disordered superconducting wire
• Search for Majorana fermions in multiband semiconducting nanowires
• Floquet generation of Majorana end modes and topological invariants
• Topology and Broken Symmetry in Floquet Systems
• Transport signatures of Floquet Majorana fermions in driven topological superconductors
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Generating Many Majorana Modes via Periodic Driving: A Superconductor Model
• Controlled Population of Floquet-Bloch States via Coupling to Bose and Fermi Baths
• Josephson radiation from gapless Andreev bound states in HgTe-based topological junctions
• Majorana bound states without vortices in topological superconductors with electrostatic defects
• Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
• Floquet symmetry-protected topological phases in cold atomic systems
• Observation of the 4$\pi$-periodic Josephson effect in indium arsenide nanowires
• Universal quantum computation on a semiconductor quantum wire network
• Floquet topological phases protected by time glide symmetry
• Counter-propagating edge modes and topological phases of a kicked quantum Hall system
• Floquet-Engineered Valleytronics in Dirac Systems
• Realization of Anomalous Floquet Insulators in Strongly-Coupled Nanophotonic Lattices
• Josephson supercurrent through the topological surface states of strained bulk HgTe
• Steady Floquet-Andreev States Probed by Tunnelling Spectroscopy
• Majorana edge modes in the Kitaev model
• Interacting invariants for Floquet phases of fermions in two dimensions
• Floquet Perturbation Theory: Formalism and Application to Low-Frequency Limit
• Topologically protected braiding in a single wire using Floquet Majorana modes
• Majorana fermion chain at the Quantum Spin Hall edge
• Fractional Josephson Effect with and without Majorana Zero Modes
• Floquet engineering to exotic topological phases in systems of cold atoms
• Floquet Majorana zero and $\pi$ modes in planar Josephson junctions
• Generating quantum multi-criticality in topological insulators by periodic driving
• Tunable Floquet Majorana Fermions in Driven Coupled Quantum Dots
• Quantized large-bias current in the anomalous Floquet-Anderson insulator
• Tunable Fragile Topology in Floquet Systems
• The Fermi-Dirac staircase occupation of Floquet bands and current rectification inside the optical gap of metals: a rigorous perspective
• Chain of Majorana States from Superconducting Dirac Fermions at a Magnetic Domain Wall
• Optically induced topological superconductivity via Floquet interaction engineering
• Floquet Majorana bound states in voltage-biased Planar Josephson Junctions
• Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence
• Hybrid-order topological odd-parity superconductors via Floquet engineering
• Anomalous Josephson effect and rectification in junctions between Floquet topological superconductors
• The Floquet Fermi Liquid

Cited by in corpus (8)

• The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation
• Josephson current signature of Floquet Majorana and topological accidental zero modes in altermagnet heterostructures
• Floquet-engineered diode performance in a Majorana-quantum dot Josephson junction
• Asymmetry-induced radiative heat transfer in Floquet systems
• Ultra-critical Floquet Non-Fermi Liquid
• Time-resolved ARPES and optical transport properties of irradiated twisted bilayer graphene in steady-state
• Dissipation-Shaped Quantum Geometry in Nonlinear Transport
• Green Function Invariants for Floquet Topological Superconductivity Induced by Proximity Effects