Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals

TL;DR

This paper establishes a bulk-hinge correspondence for higher-order topological phases with rotoinversion symmetry, enabling the prediction of chiral hinge modes and proposing a new class of higher-order Weyl semimetals characterized by symmetry eigenvalues.

Contribution

It introduces a method to determine hinge modes from symmetry eigenvalues and proposes higher-order Weyl semimetals with unique hinge and surface states.

Findings

Chiral hinge modes emerge from $C_{4} ext{I}$ eigenvalues.

Higher-order Weyl semimetals with hinge and Fermi-arc states are proposed.

Topological invariants are determined by symmetry eigenvalues.

Abstract

We give a bulk-hinge correspondence for higher-order topological phases protected by rotoinversion $C_{4}\mathcal{I}$ symmetry in magnetic systems. Our approach allows us to show the emergence of the chiral hinge modes only from the information of the $C_{4}\mathcal{I}$ eigenvalues at the high-symmetry points in the Brillouin zone. In addition, based on the bulk-hinge correspondence, we propose a class of higher-order Weyl semimetals (HOWSMs) being Weyl semimetals with hinge modes and Fermi-arc surface states. The HOWSM is characterized by topological invariants for three-dimensional higher-order topological insulators, and the topological invariants are determined by the $C_{4}\mathcal{I}$ symmetry eigenvalues at the high-symmetry points. This HOWSM has chiral hinge modes as a direct consequence of the three-dimensional higher-order topology in the bulk.