Three-dimensional topological magnon systems

Recently, magnonic analogs of spin Hall insulators in two dimensions have been proposed theoretically [1]. In our previous work, we defined a Z₂ topological invariant for them and proposed the first model of a magnonic analog of a spin Hall insulator without spin conservation [2].
Building on this previous work, in this study, we propose a concept of three-dimensional (3D) topological magnon systems characterized by a set of Z₂ topological invariants [3]. They can be thought of as magnonic analogs of 3D topological insulators. One of the models proposed is a bosonic counterpart of the Fu-Kane-Mele model, which is found to exhibit three distinct phases analogous to strong topological, weak topological, and trivial insulator phases. We also discuss a possible realization of the thermal Hall effect of surface Dirac magnons in the presence of a magnetic field.
[1] V. A. Zyuzin and A. A. Kovalev, Phys. Rev. Lett. 117, 217203 (2016).
[2] H. Kondo, Y. Akagi, and H. Katsura, Phys. Rev. B 99, 041110(R) (2019).
[3] H. Kondo, Y. Akagi, and H. Katsura, Phys. Rev. B 100, 144401 (2019) [selected as Editor’s Suggestion].