Magnetic second-order topological insulators and semimetals

TL;DR

This paper introduces magnetic second-order topological insulators and semimetals, demonstrating how magnetization can gap surface states and preserve hinge and corner states, revealing new topological phases with potential applications.

Contribution

It proposes magnetic SOTIs and semimetals, showing how magnetization affects surface, hinge, and corner states, and introduces a layered construction for topological semimetals.

Findings

Magnetization gaps surface states in 3D topological insulators.

Corner states in 2D magnetic SOTIs remain robust with magnetization.

Layered 2D magnetic SOTIs form magnetic second-order topological semimetals with robust hinge-arc states.

Abstract

We propose magnetic second-order topological insulators (SOTIs). First, we study a three-dimensional model. It is pointed out that the previously proposed topological hinge insulator has actually surface states along the [001] direction in addition to hinge states. We gap out these surface states by introducing magnetization, obtaining a SOTI only with hinge states. The bulk topological number is the $Z_2$ index protected by the combined symmetry of the four-fold rotation and the inversion symmetry. We next study two dimensional magnetic SOTIs, where the corner states are robust also in the presence of the magnetization. Finally, we construct a magnetic second-order topological semimetals by layering the two-dimensional magnetic SOTIs, where hinge-arc states are robust also in the presence of the magnetization.