Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence

Abstract

One-dimensional Floquet topological superconductors possess two types of degenerate Majorana edge modes at zero and $\pi$ quasieneriges, leaving more room for the design of boundary time crystals and quantum computing schemes than their static counterparts. In this work, we discover Floquet superconducting phases with large topological invariants and arbitrarily many Majorana edge modes in periodically driven Kitaev chains. Topological winding numbers defined for the Floquet operator and Floquet entanglement Hamiltonian are found to generate consistent predictions about the phase diagram, bulk-edge correspondence and numbers of zero and $\pi$ Majorana edge modes of the system under different driving protocols. The bipartite entanglement entropy further show non-analytic behaviors around the topological transition point between different Floquet superconducting phases. These general features are demonstrated by investigating the Kitaev chain with periodically kicked pairing or hopping amplitudes. Our discovery reveals the rich topological phases and many Majorana edge modes that could be brought about by periodic driving fields in one-dimensional superconducting systems. It further introduces a unified description for a class of Floquet topological superconductors from their quasienergy bands and entanglement properties.

37pages, 9 figures, close to the published version

References in corpus (23)

• Photovoltaic Hall effect in graphene
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Pseudospin-selective Floquet band engineering in black phosphorus
• Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Controlling a magnetic Feshbach resonance with laser light
• Topological characterizations of an extended Su-Schrieffer-Heeger model
• Measurement of a topological edge invariant in a microwave network
• Quantized Adiabatic Transport in Momentum Space
• Majorana modes and $p$-wave superfluids for fermionic atoms in optical lattices
• Floquet Semimetal with Floquet-band Holonomy
• Non-Hermitian Floquet Topological Matter -- A Review
• Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice
• Topological swing in Bloch oscillations
• Topological properties of Floquet winding bands in a photonic lattice
• Topological characterization and stability of Floquet Majorana modes in Rashba nanowire
• Observation of Floquet topological phases with large Chern numbers
• Anomalous Josephson effect and rectification in junctions between Floquet topological superconductors
• Floquet band engineering with Bloch oscillations
• Entanglement spectrum and entropy in Floquet topological matter
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Detecting Topological phase transitions in a double kicked quantum rotor

Cited by in corpus (11)

• Non-Hermitian Floquet Topological Matter -- A Review
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Anomalous topological edge modes in a periodically-driven trimer lattice
• Josephson-Current Signatures of Unpaired Floquet Majorana Bound States
• Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors
• Floquet-engineered diode performance in a Majorana-quantum dot Josephson junction
• Quantum geometry and geometric entanglement entropy of one-dimensional Floquet topological matter
• Dynamical Chiral Symmetry and Symmetry-Class Conversion in Floquet Topological Insulators
• Multiple tunable real-space degeneracies in graphene irradiated by twisted light
• Anomalous wave-packet transport on boundaries of Floquet topological systems
• Zero and Nonzero Energy Majorana Modes in an Extended Kitaev Chain