Testing topological phase transitions in Kitaev materials under in-plane magnetic fields: Application to α-RuCl_{3}

Material realization of the non-Abelian Kitaev spin liquid phase—an example of Ising topological order (ITO)—has been the subject of intense research in recent years. The 4d honeycomb Mott insulator α-RuCl_{3} has emerged as a leading candidate, as it enters a field-induced magnetically disordered state where a half-integer quantized thermal Hall conductivity κ_{xy} was reported. Further, a recent report of a sign change in the quantized κ_{xy} across a certain crystallographic direction is strong evidence for a topological phase transition between two ITOs with opposite Chern numbers. Although this is a fascinating result, independent verification remains elusive, and one may ask if there is a thermodynamic quantity sensitive to the phase transition. Here we propose that the magnetotropic coefficient k would serve such a purpose. We report a singular feature in k that indicates a topological phase transition across the b[over ̂]-axis where ITO is prohibited by a C_{2} symmetry. If the transition in α-RuCl_{3} is indeed a direct transition between ITOs, or is a more broad realization of a topological phase transition, then this feature in k should be observable. Implications of C_{2} symmetry on other experimental quantities are also discussed.