Topological honeycomb magnon Hall effect: A calculation of thermal Hall conductivity of magnetic spin excitations

Quite recently, magnon Hall effect of spin excitations has been observed experimentally on the kagome and pyrochlore lattices. Thermal Hall conductivity $\kappa^{xy}$, changes sign as a function of magnetic field or temperature on the kagome lattice, and $\kappa^{xy}$ changes sign upon reversing the sign of the magnetic field on the pyrochlore lattice. Motivated by these recent exciting experimental observations, we theoretically propose a simple realization of magnon Hall effect in a two-band model on the honeycomb lattice. The magnon Hall effect of spin excitations arises in the usual way via the breaking of inversion symmetry of the lattice, however, by a next-nearest-neighbour Dzyaloshinsky-Moriya (DM) interaction. We find that $\kappa^{xy}$ has a fixed sign for all parameter regimes considered. These results are in contrast to the Lieb, kagome and pyrochlore lattices. We further show that the low-temperature dependence on the magnon Hall conductivity follows a $T^{2}$ law, as opposed to the kagome and pyrochlore lattices. These results suggest an experimental procedure to measure thermal Hall conductivity within a class of 2D honeycomb quantum magnets and ultracold atoms trapped in honeycomb optical lattice.