Floquet generation of Second Order Topological Superconductor

TL;DR

This paper proposes a theoretical method to generate second-order topological superconductors with Majorana corner modes using Floquet engineering, involving periodic symmetry-breaking drives in a quantum spin Hall insulator with superconductivity.

Contribution

It introduces two Floquet protocols to realize strong and weak second-order topological superconducting phases with Majorana corner modes, characterized by Floquet topological invariants.

Findings

First protocol yields four zero-energy Majorana corner modes.

Second protocol can produce eight zero-energy Majorana corner modes.

Topological phases characterized by Floquet quadrupolar moment and Wannier spectrum.

Abstract

We theoretically investigate the Floquet generation of second-order topological superconducting (SOTSC) phase, hosting Majorana corner modes (MCMs), considering a quantum spin Hall insulator (QSHI) with proximity induced superconducting $s$-wave pairing in it. Our dynamical prescription consists of the periodic kick in time-reversal symmetry breaking in-plane magnetic field and four-fold rotational symmetry breaking mass term while these Floquet MCMs are preserved by anti-unitary particle-hole symmetry. The first driving protocol always leads to four zero energy MCMs (i.e. one Majorana per corner) as a sign of a {\it{strong}} SOTSC phase. Interestingly, the second protocol can result in a {\it{weak}} SOTSC phase, harbouring eight zero energy MCMs (two Majorana states per corner), in addition to the {\it{strong}} SOTSC phase. We characterize the topological nature of these phases by Floquet quadrupolar moment and Floquet Wannier spectrum. We believe that relying on the recent experimental advancement in the driven systems and proximity induced superconductivity, our schemes may be possible to test in the future.