Intrinsic Thermal Hall Effect in Mott Insulators

TL;DR

This paper demonstrates that Mott insulators can exhibit a finite thermal Hall effect under certain conditions, challenging previous assumptions and highlighting the importance of symmetry breaking and magnon interactions.

Contribution

The study shows that a simple Mott insulator can support a finite thermal Hall effect when specific symmetry-breaking conditions are met, using quantum Monte Carlo simulations and semi-classical analysis.

Findings

Finite thermal Hall effect observed in Hubbard model with non-zero t' and magnetic field.

Spin-only models with non-interacting magnons do not support thermal Hall effect.

Symmetry breaking is necessary for the thermal Hall effect in Mott insulators.

Abstract

In light of recent experimental data indicating a substantial thermal Hall effect in square lattice antiferromagnetic Mott insulators, we investigate whether a simple Mott insulator can sustain a finite thermal Hall effect. We verify that the answer is "no" if one performs calculations within a spin-only low-energy effective spin model with non-interacting magnons. However, by performing determinant quantum Monte Carlo simulations, we show the single-band $t$-$t'$-$U$ Hubbard model coupled to an orbital magnetic field does support a finite thermal Hall effect when $t' \neq 0$ and $B \neq 0$ in the Mott insulating phase. We argue that the (carrier agnostic) necessary conditions for observing a finite thermal Hall effect are time-reversal and particle-hole symmetry breaking. By considering magnon-magnon scattering using a semi-classical Boltzmann analysis, we illustrate a physical mechanism by which finite transverse thermal conductivity may arise, consistent with our symmetry argument and numerical results. Our results contradict the conventional wisdom that square and triangular lattices with SU(2) symmetry do not support a finite thermal Hall effect and call for a critical re-examination of thermal Hall effect data in insulating magnets, as the magnon contribution should not be excluded a priori.