Geometry dependence of the thermal Hall effect in chiral spin liquids

Recent thermal-transport experiments on the Kitaev magnet $\alpha$-RuCl${}_3$ highlight the challenge in identifying chiral quantum spin liquids through their quantized thermal Hall effect. Here, we propose that variations in the underlying sample geometry – for example, the introduction of appropriate constrictions – reveal unique aspects of the thermal Hall effect and can be used to determine its origin. By studying standard phenomenological heat-transport equations based on minimal assumptions, we show that, whereas a conventional thermal Hall effect due to, e.g., phonons or magnons is completely geometry independent, a thermal Hall effect originating from a chiral fermion edge mode is significantly enhanced by constrictions at low temperatures. This unique geometry-dependent signature provides a practical approach for identifying chiral spin liquids in candidate materials like $\alpha$-RuCl${}_3$ using currently available thermal-transport experiments.