Majorana corner modes and flat-band Majorana edge modes in superconductor/topological-insulator/superconductor junctions

TL;DR

This paper explores higher-order topological superconductivity in a superconductor/topological insulator/superconductor junction, revealing Majorana corner modes and flat-band Majorana edge modes induced by magnetic fields, with potential stability in thicker films.

Contribution

It demonstrates the realization of Majorana corner modes and flat-band Majorana edge modes in a 2D Josephson junction with a topological insulator, advancing understanding of higher-order topological superconductivity.

Findings

Majorana corner modes can be achieved with magnetic fields.

A 2D nodal phase supports flat-band Majorana edge modes.

Zero-energy Majorana modes are stable with increasing TI thickness.

Abstract

Recently, superconductors with higher-order topology have stimulated extensive attention and research interest. Higher-order topological superconductors exhibit unconventional bulk-boundary correspondence, thus allow exotic lower-dimensional boundary modes, such as Majorana corner and hinge modes. However, higher-order topological superconductivity has yet to be found in naturally occurring materials. In this work, we investigate higher-order topology in a two-dimensional Josephson junction comprised of two $s$-wave superconductors separated by a topological insulator thin film. We found that zero-energy Majorana corner modes, a boundary fingerprint of higher-order topological superconductivity, can be achieved by applying magnetic field. When an in-plane Zeeman field is applied to the system, two corner states appear in the superconducting junction. Furthermore, we also discover a two dimensional nodal superconducting phase which supports flat-band Majorana edge modes connecting the bulk nodes. Importantly, we demonstrate that zero-energy Majorana corner modes are stable when increasing the thickness of topological insulator thin film.