Thermal Hall effect in square-lattice spin liquids*

The extension of the notion of a topology-driven Hall effect to charge-neutral excitations has been an exciting theoretical development. Motivated by recent experimental observations in high-Tc cuprate superconductors in a magnetic field, we study the thermal Hall conductivity in materials with topological order, focusing on the contribution from the deconfined neutral gapped spinons in the insulating state. More specifically, we examine different Schwinger-boson mean-field ansätze for the Heisenberg antiferromagnet on the square lattice, allowing for both Dzyaloshinskii-Moriya interactions and additional terms that break time-reversal and reflection symmetries but preserve their product. We show that the bosonic bands acquire nontrivial Chern numbers and evaluate the thermal Hall coefficient. On top of a significantly enhanced conductivity, which should yield a sizable experimental signal, we also observe an anomalous contribution.