Symmetry Analysis of Tensors for the Honeycomb Lattice of Edge-Sharing Octahedra

We obtain the most general form of rank-2 and rank-3 tensors allowed by the symmetries of a honeycomb lattice of edge-sharing octahedra (such as alpha-RuCl3 and CrI3). We highlight some unexpected results, including the equality of a fully-longitudinal component to a partially-transverse component. Finally, we compare these findings to a recent thermal Hall experiment in alpha-RuCl3 and make predictions for systems with topological bands.