Topological properties of domain walls in antiferromagnetic topological insulators

Motivated by the study of stacking faults in weak topological insulators and the observation of magnetic domain walls in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>MnBi</a:mi><a:mrow><a:mn>2</a:mn><a:mi>n</a:mi></a:mrow></a:msub><a:msub><a:mi>Te</a:mi><a:mrow><a:mn>3</a:mn><a:mi>n</a:mi><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:msub></a:mrow></a:math>, we explore the topological properties of magnetic domain walls in antiferromagnetic topological insulators. We develop two tight-binding models for two different types of antiferromagnetic topological insulators: the first type obtained by adding antiferromagnetic order to a strong topological insulator and another built from stacked Chern insulating layers with alternating Chern numbers. Both systems are dual topological insulators, i.e., they are at the same time antiferromagnetic and crystalline topological insulators, but differ by the type of mirror symmetry protecting the crystalline phase: spinful versus spinless. We show that in the spinful case the mirror Chern number is invariant under time reversal and that it changes sign in the spinless case. This influences the properties of the two systems in the presence of a magnetic domain wall, which we model as an interface between two regions of opposite magnetization. In the first type, the bulk of the magnetic domain wall is gapped but the defect will host chiral edge states when it ends on an external ferromagnetic surface. In the second, due to the change in the sign of the mirror Chern number, the magnetic domain wall is a two-dimensional (2D) embedded semimetal with 2D gapless states protected by mirror symmetry. Our results show that magnetic domain walls can be a source of nontrivial topology, allowing one to generate and manipulate gapless states within the bulk and the ferromagnetic surfaces of antiferromagnetic topological insulators.