Three-dimensional topological magnon systems

Abstract

Here, the authors propose the concept of topological magnon systems, which are bosonic generalizations of three-dimensional topological insulators. Introducing the notion of pseudo-time-reversal symmetry, they define the ${\mathcal{Z}}_{2}$ topological invariants, whose values correspond to the presence or absence of symmetry-protected surface states. Since bosonic systems described by the Bogoliubov--de Gennes Hamiltonian are intrinsically non-Hermitian, the definition differs from that of fermionic systems. In addition, they show that placing a system in proximity to a ferromagnet induces the thermal Hall effect at their interface.