Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors

Abstract

Majorana zero modes have been shown to be the simplest quasiparticles exhibiting pure odd-frequency pairing, an effect that has so far been theoretically established in the static regime. In this work, we investigate the formation of Majorana modes and odd-frequency pairing in $p$-wave spin-polarized superconductors under a time-dependent drive. We first show that the driven system hosts multiple Majorana modes emerging at zero and $\pi$, whose formation can be controlled by an appropriate tuning of the drive frequency and chemical potential, in agreement with previous studies. Then we explore the induced pair correlations and find that odd-frequency spin-polarized $s$-wave pairing is broadly induced, acquiring large values in the presence of Majorana modes. We discover that, while odd-frequency pairing is proportional to $\sim 1/\omega$ in the presence of Majorana zero modes, it is proportional to $\sim 1/(\omega -\pi \hslash /T)$ in the presence of Majorana $\pi$ modes, where $T$ is the periodicity of the drive. Furthermore, we find that the amount of odd-frequency pairing becomes larger when multiple Majorana modes appear but the overall divergent profile as a function of frequency remains. We also show that the divergent odd-frequency pairing is robust against scalar disorder. Notably, we establish a spectral bulk-boundary correspondence between the amount of boundary odd-$\omega$ pairing and the bulk topological invariants in driven chiral systems, which we show to be protected by chiral symmetry and is thus robust against disorder. Our work thus paves the way for understanding the emergent pair correlations in driven topological superconductors

19 pages, 8 figures, published version

References in corpus (81)

• Topological insulators and superconductors
• Classification of topological quantum matter with symmetries
• Search for Majorana fermions in superconductors
• Topological superconductors: a review
• Odd Triplet Superconductivity and Related Phenomena in Superconductor-Ferromagnet Structures
• Symmetry and Topology in Non-Hermitian Physics
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Majorana Zero Modes and Topological Quantum Computation
• Superconducting Spintronics
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• Introduction to topological superconductivity and Majorana fermions
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Long-range effects in superconductor-ferromagnet structures
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires
• Single particle Green's functions and interacting topological insulators
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Theory of the proximity effect in junctions with unconventional superconductors
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Floquet generation of Majorana end modes and topological invariants
• Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
• A Short Introduction to Topological Quantum Computation
• Odd-frequency superconductivity
• Majorana Fermions in superconducting wires: effects of long-range hopping, broken time-reversal symmetry and potential landscapes
• SNS junctions in nanowires with spin-orbit coupling: role of confinement and helicity on the sub-gap spectrum
• Odd-frequency pairing in normal metal/superconductor junctions
• Next steps of quantum transport in Majorana nanowire devices
• Generating Many Majorana Modes via Periodic Driving: A Superconductor Model
• Anomalous charge transport in mesoscopic triplet superconductor junctions
• Majorana Fermions and Odd-frequency Cooper Pairs in a Nano Wire
• Search for non-Abelian Majorana braiding statistics in superconductors
• Anomalous features of the proximity effect in triplet superconductors
• Majorana nanowires for topological quantum computation
• Proximity-induced unconventional superconductivity in topological insulators
• Anomalous Surface Impedance due to Odd-frequency Cooper Pairs
• Towards large-Chern-number topological phases by periodic quenching
• Odd-frequency superconducting pairing in one-dimensional systems
• Odd-frequency superconducting pairing in topological insulators
• A perspective on semiconductor-based superconducting qubits
• Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism
• Theory of Majorana zero modes in unconventional superconductors
• Superconducting proximity effect in three-dimensional topological insulators in the presence of a magnetic field
• Odd-Frequency Triplet Superconductivity at the Helical Edge of a Toplogical Insulator
• Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
• Real-space representation of winding number for one-dimensional chiral-symmetric topological insulator
• The Role of Odd-Frequency Pairing in Multiband Superconductors
• Distinguishing trivial and topological zero energy states in long nanowire junctions
• Odd-frequency superconducting pairing in junctions with Rashba spin-orbit coupling
• Theory of time reversal topological superconductivity in double Rashba wires -- symmetries of Cooper pair and Andreev bound states
• Conductance signatures of odd-frequency superconductivity in quantum spin Hall systems using a quantum point contact
• Josephson and proximity effects on the surface of a topological insulator
• Tunable hybridization of Majorana bound states at the quantum spin Hall edge
• Helical Liquids in Semiconductors
• Creation of spin-triplet Cooper pairs in the absence of magnetic ordering
• Odd-frequency superconductivity in a nanowire coupled to Majorana zero modes
• Observation of triplet superconductivity in CoSi${}_2$/TiSi${}_2$ heterostructures
• Odd-Frequency Pairs in Chiral Symmetric Systems: Spectral Bulk-Boundary Correspondence and Topological Criticality
• Odd frequency pairing of interacting Majorana fermions
• Odd-frequency pairing and proximity effect in Kitaev chain systems including topological critical point
• Odd-frequency superconductivity and Meissner effect in the doped topological insulator Bi${}_2$Se${}_3$
• Topological characterization and stability of Floquet Majorana modes in Rashba nanowire
• Multiple odd-frequency superconducting states in buckled quantum spin Hall insulators with time-reversal symmetry
• Odd-frequency superconducting pairing in Kitaev-based junctions
• Signature of odd-frequency equal-spin triplet pairing in the Josephson current on the surface of Weyl nodal loop semimetals
• Suppression of odd-frequency pairing by phase-disorder in a nanowire coupled to Majorana zero modes
• Bulk odd-frequency pairing in the superconducting Su-Schrieffer-Heeger model
• Tunneling spectroscopy and Josephson current of superconductor-ferromagnet hybrids on the surface of a 3D TI
• Theory of proximity effect in two-dimensional unconventional superconductor with Rashba spin-orbit interaction
• Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence
• Engineering anomalous Floquet Majorana modes and their time evolution in helical Shiba chain
• Large Josephson current in Weyl nodal loop semimetals due to odd-frequency superconductivity
• Hybrid-order topological odd-parity superconductors via Floquet engineering
• Anomalous Josephson effect and rectification in junctions between Floquet topological superconductors
• Generalization of spectral bulk-boundary correspondence
• Chirality polarizations and spectral bulk-boundary correspondence
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Gapless odd-frequency superconductivity induced by the Sachdev-Ye-Kitaev model
• Electronic conduction and superconducting properties of CoSi${}_2$ films on silicon--an unconventional superconductor with technological potential
• Quantum Pairing Time Orders
• Majorana modes in trapped-ion system and their Floquet engineering

Cited by in corpus (7)

• Floquet engineering spin triplet states in unconventional magnets
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Light-induced Floquet spin-triplet Cooper pairs in unconventional magnets
• Anomalous proximity effect under Andreev and Majorana bound states
• Floquet-Nambu theory of electron quantum optics with superconductors
• Dynamics of Majorana zero modes across hybrid Kitaev chain
• Odd-frequency Pairing in Josephson Junctions Coupled by Magnetic Textures