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 (25)

• Introduction to topological superconductivity and Majorana fermions
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Theory of the proximity effect in junctions with unconventional superconductors
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• 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
• Majorana Fermions and Odd-frequency Cooper Pairs in a Nano Wire
• Majorana nanowires for topological quantum computation
• 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
• Helical Liquids in Semiconductors
• Creation of spin-triplet Cooper pairs in the absence of magnetic ordering
• 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
• 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
• 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
• 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