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

TL;DR

This paper explores Floquet topological superconductors, revealing phases with many Majorana edge modes, characterized by topological invariants and entanglement spectra, expanding the understanding of driven quantum systems.

Contribution

It introduces a unified framework for analyzing Floquet topological superconductors using topological invariants and entanglement properties, demonstrating the possibility of many Majorana modes.

Findings

Discovery of Floquet phases with arbitrarily many Majorana edge modes

Topological invariants predict phase diagram and edge modes accurately

Non-analytic entanglement entropy signals topological transitions

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.