# Topological thermal Hall effect for topological excitations in spin liquid: Emergent Lorentz force on the spinons

## TL;DR

This paper proposes a mechanism where an external magnetic field induces an internal gauge flux in a U(1) spin liquid, leading to a topological thermal Hall effect for spinons, with implications for kagome lattice materials.

## Contribution

It introduces a novel understanding of how the Lorentz force acts on neutral spinons via Dzyaloshinskii-Moriya interaction, resulting in a topological thermal Hall effect.

## Key findings

- External magnetic field generates internal U(1) gauge flux for spinons.
- The mechanism differs from charge fluctuation-induced flux in Mott insulators.
- Applicable to kagome lattice spin liquids and relevant to thermal Hall transport in specific materials.

## Abstract

We study the origin of Lorentz force on the spinons in a U(1) spin liquid. We are inspired by the previous observation of gauge field correlation in the pairwise spin correlation using the neutron scattering measurement when the Dzyaloshinskii-Moriya interaction intertwines with the lattice geometry. We extend this observation to the Lorentz force that exerts on the (neutral) spinons. The external magnetic field, that polarizes the spins, effectively generates an internal U(1) gauge flux for the spinons and twists the spinon motion through the Dzyaloshinskii-Moriya interaction. Such a mechanism for the emergent Lorentz force differs fundamentally from the induction of the internal U(1) gauge flux in the weak Mott insulating regime from the charge fluctuations. We apply this understanding to the specific case of spinon metals on the kagome lattice. Our suggestion of emergent Lorentz force generation and the resulting topological thermal Hall effect may apply broadly to other non-centrosymmetric spin liquids with Dzyaloshinskii-Moriya interaction. We discuss the relevance with the thermal Hall transport in kagome materials volborthite and kapellasite.