Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors

TL;DR

This paper demonstrates how periodic driving in 2D superconductors can generate numerous Floquet second-order topological phases with multiple Majorana corner modes, controllable via system parameters, advancing quantum computation prospects.

Contribution

It introduces a method to produce diverse Floquet SOTSC phases with multiple Majorana modes and characterizes the phase transitions driven by spectral gap changes.

Findings

Multiple Floquet SOTSC phases with zero and π Majorana corner modes

Phase transitions driven by bulk and edge spectral gap closures

High controllability of phases via a single hopping parameter

Abstract

A $d$-dimensional, $n$th-order topological insulator or superconductor has localized eigenmodes at its $(d-n)$-dimensional boundaries ($n\leq d$). In this work, we apply periodic driving fields to two-dimensional superconductors, and obtain a wide variety of Floquet second-order topological superconducting (SOTSC) phases with many Majorana corner modes at both zero and $\pi$ quasienergies. Two distinct Floquet SOTSC phases are found to be separated by three possible kinds of transformations, i.e., a topological phase transition due to the closing/reopening of a bulk spectral gap, a topological phase transition due to the closing/reopening of an edge spectral gap, or an entirely different phase in which the bulk spectrum is gapless. Thanks to the strong interplay between driving and intrinsic energy scales of the system, all the found phases and transitions are highly controllable via tuning a single hopping parameter of the system. Our discovery not only enriches the possible forms of Floquet SOTSC phases, but also offers an efficient scheme to generate many coexisting Majorana zero and $\pi$ corner modes that may find applications in Floquet quantum computation.