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

Abstract

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 $\bar{3}$. Our results are relevant for two-dimensional materials, such as $\alpha$-RuCl${}_3$, CrI${}_3$, and the honeycomb iridates. We focus on the magnetic-field-dependent thermal conductivity tensor ${\kappa }_{ij}(\mathbf{H})$, 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 three-fold rotational symmetry, and make testable predictions for the thermal conductivity tensor.

arXiv comment14 pages, 5 figures, 3 tables

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• Symmetry-based requirement for the measurement of electrical and thermal Hall conductivity under an in-plane magnetic field
• Field-angle dependence of thermal Hall conductivity in magnetically ordered Kitaev-Heisenberg system
• Orbital Frustration and Emergent Flat Bands
• Electrical control of intrinsic nonlinear Hall effect in antiferromagnetic topological insulator sandwiches
• Successive topological phase transitions in two distinct spin-flop phases on the honeycomb lattice
• Contrasting magnetothermal conductivity in sibling Co-based honeycomb-lattice antiferromagnets
• Tunable spin-charge conversion in class-I topological Dirac semimetals