Z2 topological invariant for magnon spin Hall systems

ORAL

Abstract

The classification and characterization of different phases of matter based on the topology of band structures has recently attracted much attention. It is known that some of the topological phenomena in electron systems are carried over to bosonic systems [1]. However, the topological invariant of bosonic systems with time-reversal symmetry has not yet been identified, as Kramers' theorem cannot be applied to them. To address this issue, we first introduce the pseudo-time-reversal operator which ensures the existence of ``Kramers pairs'' of bosons. Then, we define the Z2 topological invariant for magnon spin Hall systems [2] using the Berry connection and curvature for bosons, which are different from those of electrons [3]. Furthermore, we propose two magnetic models with magnon bands carrying the nontrivial Z2 topological invariant. We also demonstrate that the presence (absence) of helical edge states corresponds to the nontrivial (trivial) value of the Z2 topological invariant.

[1] H. Katsura, N. Nagaosa, and P. A. Lee, Phys. Rev. Lett. 104, 066403 (2010).
[2] H. Kondo, Y. Akagi, and H. Katsura, arXiv:1808.09149.
[3] R. Matsumoto, R. Shindou, and S. Murakami, Phys. Rev. B 89,054420 (2014).

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Presenters

  • Hiroki Kondo

    Department of Physics, University of Tokyo

Authors

  • Hiroki Kondo

    Department of Physics, University of Tokyo

  • Yutaka Akagi

    Department of Physics, University of Tokyo

  • Hosho Katsura

    Physics, University of Tokyo, Department of Physics, University of Tokyo, University of Tokyo, Department of Physics, The University of Tokyo