  In the conventional ferromagnetic systems, topological magnon bands and
thermal Hall effect are due to the Dzyaloshinskii-Moriya interaction (DMI). In
principle, however, the DMI is either negligible or it is not allowed by
symmetry in some quantum magnets. Therefore, we expect that topological magnon
features will not be present in those systems. In addition, quantum magnets on
the triangular-lattice are not expected to possess topological features as the
DMI or spin-chirality cancels out due to equal and opposite contributions from
adjacent triangles. Here, however, we predict that the isomorphic frustrated
honeycomb-lattice and bilayer triangular-lattice antiferromagnetic system will
exhibit topological magnon bands and topological thermal Hall effect in the
absence of an intrinsic DMI. These unconventional topological magnon features
are present as a result of magnetic-field-induced non-coplanar spin
configurations with nonzero scalar spin chirality. The relevance of the results
to realistic bilayer triangular antiferromagnetic materials are discussed.
