# Thermal Hall effect in square-lattice spin liquids: A Schwinger boson mean-field study

## TL;DR

This study investigates the thermal Hall effect in square-lattice spin liquids using Schwinger boson mean-field theory, revealing how scalar spin chiralities induce topological spinon bands and enhance thermal Hall conductivity.

## Contribution

It introduces a detailed analysis of how scalar spin chiralities and Dzyaloshinskii-Moriya interactions influence the thermal Hall effect in square-lattice spin liquids.

## Key findings

- Scalar spin chiralities lead to nontrivial Chern bands for spinons.
- Enhanced thermal Hall conductivity is observed due to topological spinon bands.
- States with magnetic order also show significant thermal Hall responses.

## Abstract

Motivated by recent transport measurements in high-$T_c$ cuprate superconductors in a magnetic field, we study the thermal Hall conductivity in materials with topological order, focusing on the contribution from neutral spinons. Specifically, different Schwinger boson mean-field ans\"{a}tze for the Heisenberg antiferromagnet on the square lattice are analyzed. We allow for both Dzyaloshinskii-Moriya interactions, and additional terms associated with scalar spin chiralities that break time-reversal and reflection symmetries, but preserve their product. It is shown that these scalar spin chiralities, which can either arise spontaneously or are induced by the orbital coupling of the magnetic field, can lead to spinon bands with nontrivial Chern numbers and significantly enhanced thermal Hall conductivity. Associated states with zero-temperature magnetic order, which is thermally fluctuating at any $T>0$, also show a similarly enhanced thermal Hall conductivity.