Journal
PHYSICAL REVIEW B
Volume 99, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.99.041110
Keywords
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Funding
- JSPS KAKENHI [JP17K14352, JP18H04478, JP18K03445, JP18H04220]
- JSPS through Program for Leading Graduate Schools (ALPS)
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We propose a definition of a Z(2) topological invariant for magnon spin Hall systems which are the bosonic analog of two-dimensional topological insulators in class AII. The existence of Kramers pairs in these systems is guaranteed by pseudo-time-reversal symmetry which is the same as time-reversal symmetry up to some unitary transformation. The Z(2) index of each Kramers pair of bands is expressed in terms of the bosonic counterparts of the Berry connection and curvature. We construct explicit examples of magnon spin Hall systems and demonstrate that our Z(2) index precisely characterizes the presence or absence of helical edge states. The proposed Z(2) index and the formalism developed can be applied not only to magnonic systems but also to other noninteracting bosonic systems.
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