Majorana Corner Modes and Flat-Band Majorana Edge Modes in Superconductor/Topological-Insulator/Superconductor Junctions

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. 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 find 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 modes 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.