Topological phase transition induced by magnetic proximity effect in two dimensions

Abstract

We study the magnetic proximity effect on a two-dimensional topological insulator in a CrI${}_3$/SnI${}_3$/CrI${}_3$ trilayer structure. From first-principles calculations, the BiI${}_3$-type SnI${}_3$ monolayer without spin-orbit coupling has Dirac cones at the corners of the hexagonal Brillouin zone. With spin-orbit coupling turned on, it becomes a topological insulator, as revealed by a non-vanishing $Z_2$ invariant and an effective model from symmetry considerations. Without spin-orbit coupling, the Dirac points are protected if the CrI${}_3$ layers are stacked ferromagnetically, and are gapped if the CrI${}_3$ layers are stacked antiferromagnetically, which can be explained by the irreducible representations of the magnetic space groups $C_{3i}^1$ and $C_{3i}^1(C_3^1)$, corresponding to ferromagnetic and antiferromagnetic stacking, respectively. By analyzing the effective model including the perturbations, we find that the competition between the magnetic proximity effect and spin-orbit coupling leads to a topological phase transition between a trivial insulator and a topological insulator.

11 pages, 5 figures, 2 tables. Accepted by Journal of Physics: Condensed Matter

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