Hierarchy of topological superconductivity generated via heterostructures of unconventional $p$-wave magnets

Abstract

A theoretical framework is proposed to engineer both first and second-order topological superconducting phases in a two-dimensional (2D) heterostructure, consisting of a quantum spin Hall insulator (QSHI) and an unconventional $p$-wave magnet in presence of proximity-induced $s$-wave superconducting pairing. Our analysis establishes that the transitions between the trivial and topological superconducting (TSC) phases can be regulated though the parameters of $p$-wave magnet. Presence of chiral symmetry leads to the characterization of both types of TSC phases by the respective invariants, one-dimensional winding number and quadrupolar winding number. These results are supplemented by an analytical effective low-energy edge theory that yields a deeper insight into the emergence of the different topological phases of the system. Bulk pairing analysis reveals the competition between the effective $(p_x+p_y)$ and $(p_x+i{p}_y)$ type pairings that are governed by the intrinsic spin-orbit coupling inherited to the QSHI and spin-split bands of the $p$-wave magnet, respectively.

arXiv comment6 Pages + 5 PDF Figures (Main Text) and 6 Pages (Supplementary Material); Comments are welcome