Hierarchy of higher-order topological superconductors in three dimensions

TL;DR

This paper proposes a three-dimensional model for higher-order topological superconductors, revealing a hierarchy of phases with Majorana modes, and demonstrates how perturbations and Floquet engineering can control these exotic states.

Contribution

It introduces a simple fermionic model for 3D HOTSCs with a hierarchy of phases, including Majorana hinge and corner modes, and explores their manipulation via perturbations and Floquet engineering.

Findings

Hierarchy of HOTSC phases realized in a single 3D model

Majorana hinge modes appear above a threshold perturbation

Majorana corner modes emerge with infinitesimal second-kind perturbation

Abstract

After exploring much on two-dimensional higher-order topological superconductors (HOTSCs) hosting Majorana corner modes (MCMs) only, we propose a simple fermionic model based on a three-dimensional topological insulator proximized with $s$-wave superconductor to realize Majorana hinge modes (MHMs) followed by MCMs under the application of appropriate Wilson-Dirac perturbations. We interestingly find that the second-order topological superconductor, hosting MHMs, appears above a threshold value of the first type perturbation while the third-order topological superconducting phase, supporting MCMs, immediately arises incorporating infinitesimal perturbation of the second kind. Thus, a hierarchy of HOTSC phases can be realized in a single three-dimensional model. Additionally, the application of bulk magnetic field is found to be instrumental in manipulating the number of MHMs, leaving the number for MCMs unaltered. We analytically understand these above-mentioned numerical findings by resorting to the low energy model. We further characterize these topological phases with a distinct structure of the Wannier spectra. From the practical point of view, we manifest quantized transport signatures of these higher-order modes. Finally, we construct Floquet engineering to generate the hierarchy of HOTSC phases by kicking the same perturbations as considered in their static counterpart.