Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor

TL;DR

This paper proposes a 2D magnetic topological insulator on a high-temperature superconductor as a platform for Majorana corner states, revealing their topological origin and potential for non-Abelian braiding.

Contribution

It introduces a second-order topological superconductor model with Majorana corner states in a 2D hybrid system, analyzing the role of pairing symmetry and magnetic exchange.

Findings

Majorana bound states are localized at corners due to pairing symmetry.

Topological phase diagrams depend on magnetic exchange and pairing amplitude.

Edge theory explains the origin of corner Majorana states.

Abstract

Conventional $n$-dimensional topological superconductors (TSCs) have protected gapless $(n - 1)$-dimensional boundary states. In contrast to this, second-order TSCs are characterized by topologically protected gapless $(n - 2)$-dimensional states with usual gapped $(n - 1)$-boundaries. Here, we study a second-order TSC with a two-dimensional (2D) magnetic topological insulator (TI) proximity-coupled to a high-temperature superconductor, where Majorana bound states (MBSs) are localized at the corners of a square sample with gapped edge modes. Due to the mirror symmetry of the hybrid system considered here, there are two MBSs at each corner for both cases: d-wave and $s_{\pm}$-wave superconducting pairing. We present the corresponding topological phase diagrams related to the role of the magnetic exchange interaction and the pairing amplitude. A detailed analysis, based on edge theory, reveals the origin of the existence of MBSs at the corners of the 2D sample, which results from the sign change of the Dirac mass emerging at the intersection of any two adjacent edges due to pairing symmetry. Possible experimental realizations are discussed. Our proposal offers a promising platform for realizing MBSs and performing possible non-Abelian braiding in 2D systems.