Topological surfaces of domain wall-decorated antiferromagnetic topological insulator MnBi$_{2n}$Te$_{3n+1}$

TL;DR

This paper investigates how domain walls in antiferromagnetic topological insulators affect their surface states, revealing conditions under which these states become gapless or remain gapped, and identifying a topological transition related to magnetic fluctuations.

Contribution

It introduces a non-statistical index called the Ising moment that determines the surface gap and uncovers a surface delocalization transition influenced by magnetic fluctuations and symmetry class crossover.

Findings

Surface states can be gapless even when $S$ symmetry is broken.

A topological transition occurs near zero energy due to symmetry class crossover.

Surface delocalization transition is linked to magnetic fluctuation bounds.

Abstract

Antiferromagnetic topological insulators harbor topological in-gap surface states protected by an anti-unitary $S$ symmetry, which is broken by the inevitable presence of domain walls. Whether an antiferromagnetic topological insulator with domain walls is gapless and metallic on its topological surfaces remains to be elucidated. We show that a single non-statistical index characterizing the magnetic order of domain wall-decorated antiferromagnetic topological insulator, referred to as the Ising moment, determines the topological surface gap, which can be zero even when the $S$ symmetry is manifestly broken. In the thermodynamic limit, the topological surface states tend to be gapless when magnetic fluctuation is bounded. In this case, the Lyapunov exponent of the surface transfer matrix reveals a surface delocalization transition near the zero energy due to a crossover from orthogonal to chiral orthogonal symmetry class. Spectroscopic and transport measurements on the surface states will reveal the critical behavior of the transition, which in return bears on the nature of antiferromagnetic domains walls.