Second-order topological superconductor via noncollinear magnetic texture

TL;DR

This paper proposes a theoretical method to realize a 2D second-order topological superconductor with Majorana corner modes using heterostructures with noncollinear magnetic textures, supported by analytical and numerical analysis.

Contribution

It introduces a novel heterostructure design incorporating magnetic textures to stabilize the second-order topological superconducting phase, with detailed theoretical and numerical validation.

Findings

Stabilization of Majorana corner modes at four corners.

Characterization of bulk topology via quadrupole moment.

Effective low-energy Hamiltonian reveals magnetic texture effects.

Abstract

We put forth a theoretical framework for engineering a two-dimensional (2D) second-order topological superconductor (SOTSC) by utilizing a heterostructure: incorporating noncollinear magnetic textures between an $s$-wave superconductor and a 2D quantum spin Hall insulator. It stabilizes the higher order topological superconducting phase, resulting in Majorana corner modes (MCMs) at four corners of a 2D domain. The calculated non-zero quadrupole moment characterizes the bulk topology. Subsequently, through a unitary transformation, an effective low-energy Hamiltonian reveals the effects of magnetic textures, resulting in an effective in-plane Zeeman field and spin-orbit coupling. This approach provides a qualitative depiction of the topological phase, substantiated by numerical validation within exact real-space model. Analytically calculated effective pairings in the bulk illuminate the microscopic behavior of the SOTSC. The comprehension of MCM emergence is supported by a low-energy edge theory, which is attributed to the interplay between effective pairings of $(p_x + p_y)$-type and $(p_x + i p_y)$-type. Our extensive study paves the way for practically attaining the SOTSC phase by integrating noncollinear magnetic textures.