Momentum-inversion symmetry breaking on the Fermi surface of magnetic topological insulators

TL;DR

This paper proposes a new symmetry-based method to detect surface magnetism in magnetic topological insulators by analyzing momentum-inversion symmetry violations in their Fermi surface structure.

Contribution

It introduces a novel symmetry criterion based on momentum-inversion symmetry breaking to probe surface magnetism in magnetic topological insulators.

Findings

Surface band structures violate momentum-inversion symmetry due to combined time-reversal and inversion symmetry breaking.

The Fermi surface exhibits a three-fold rotational symmetry instead of six-fold, indicating surface magnetism.

The symmetry violation is most prominent along the Γ-K direction on the (0001) plane.

Abstract

Magnetic topological insulators (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ were anticipated to exhibit magnetic energy gaps while recent spectroscopic studies did not observe them. Thus, magnetism on the surface is under debate. In this work, we propose another symmetry criterion to probe the surface magnetism. Because of both time-reversal symmetry-breaking and inversion symmetry-breaking, we demonstrate that the surface band structure violates momentum-inversion symmetry and leads to a three-fold rather than six-fold rotational symmetry on the Fermi surface if corresponding surface states couple strongly to the surface magnetism. Such a momentum-inversion symmetry violation is significant along the $\Gamma-K$ direction for surface bands on the (0001) plane.