Symmetry analysis of tensors in the honeycomb lattice of edge-sharing octahedra

We obtain the most general forms of rank-2 and rank-3 tensors allowed by the crystal symmetries of the honeycomb lattice of edge-sharing octahedra for crystals belonging to different crystallographic point groups, including the monoclinic point group 2/m and the trigonal (or rhombohedral) point group (3) over bar. Our results are relevant for two-dimensional materials, such as alpha-RuCl3, CrI3, and the honeycomb iridates. We focus on the magnetic-field-dependent thermal conductivity tensor kappa(ij)(H), which describes a system's longitudinal and thermal Hall responses, for the cases when the magnetic field is applied along high-symmetry directions, perpendicular to the plane and in the plane. We highlight some unexpected results, such as the equality of fully longitudinal components to partially transverse components in rank-3 tensors for systems with threefold rotational symmetry, and make testable predictions for the thermal conductivity tensor.