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arXiv:2410.14863 · Physical Review Letters

Intrinsic Thermal Hall Effect in Mott Insulators

Jixun K. Ding, Emily Z. Zhang, Wen O. Wang, Tessa Cookmeyer, Brian Moritz, Yong Baek Kim, Thomas Devereaux

Published May 27, 2025• 2 citations
arXivHTMLPDF

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 noninteracting 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^{'}≠0 and B≠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 semiclassical 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 indicate that square and triangular lattices with SU(2) symmetry can support a finite thermal Hall effect and call for a critical reexamination of thermal Hall effect data in insulating magnets, as the magnon contribution should not be excluded a priori.

DOI
10.1103/2729-nmyh

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Whether or not anomalies in the thermal conductivity from insulating cuprates can be attributed to antiferromagnetic order and magnons in a 2D Mott insulator remains an intriguing open question. To shed light on this issue, we investigate the thermal conductivity κ\kappaκ and specific heat cvc_vcv​ of the half-filled 2D single-band Hubbard model using the numerically exact determinant quantum Monte Carlo algorithm and maximum entropy analytic continuation. Both cvc_vcv​ and κ\kappaκ possess two peaks as a function of temperature, with scales related to the Hubbard interaction energy UUU and spin superexchange energy JJJ, respectively. At low temperatures where the charge degrees of freedom are gapped-out, our results for the contribution to both cvc_vcv​ and the Drude weight associated with κ\kappaκ from the kinetic energy agree well with spin-wave theory for the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg model.
Whether or not anomalies in the thermal conductivity in insulating cuprates can be attributed to antiferromagnetic order and magnons in a 2D Mott insulator remains an intriguing open question. To shed light on this issue, we investigate the thermal conductivity $\ensuremath{\kappa}$ and its relationship with the specific heat cv{c}_{v}cv​ in the half-filled 2D single-band Hubbard model, using the numerically exact determinant quantum Monte Carlo algorithm and maximum entropy analytic continuation. At low temperatures where the charge degrees of freedom are gapped-out and cv{c}_{v}cv​ exhibits a clear magnon peak, we observe that thermal conductivity $\ensuremath{\kappa}$ also tends to form a peak at similar temperatures. Reducing temperature further produces a sharp upturn in $\ensuremath{\kappa}$, associated with an increasing mean-free path. We identify this as the high-temperature side of the anomalous peak in insulating cuprates, where the mean-free path eventually is cut off by other scattering effects, including phonons, disorder, and physical size. Different scattering effects in our model are identified and analyzed in the thermal diffusivity.
The Hall coefficient exhibits anomalous behavior in lightly doped Mott insulators. For strongly interacting electrons its computation has been challenged by analytical and numerical obstacles. We calculate the leading contributions in the recently derived thermodynamic formula for the Hall coefficient. We obtain its doping and temperature dependence for the square lattice tJ-model at high temperatures. The second order corrections are evaluated to be negligible. Quantum Monte Carlo sampling extends our results to lower temperatures. We find a divergence of the Hall coefficient toward the Mott limit and a sign reversal relative to Boltzmann equation's weak scattering prediction. The Hall current near the Mott phase is carried by a low density of spin-entangled vacancies, which should constitute the Cooper pairs in any superconducting phase at lower temperatures.
Motivated by recent transport measurements in high-Tc{T}_{c}Tc​ 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\"atze 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>0T>0T>0, also show a similarly enhanced thermal Hall conductivity.
In the pseudogap phase of the cuprate, a thermal Hall response of neutral objects has been recently detected experimentally, which continuously persists into the antiferromagnetic insulating phase. In this paper, we study the transport properties of neutral spinons as the elementary excitation of a doped Mott insulator, which is governed by a mutual Chern-Simons topological gauge structure. We show that such a chiral spinon as a composite of an S = 1 / 2 spin sitting at the core of a supercurrent vortex, can contribute to the thermal Hall effect, thermopower, and Hall effect due to its intrinsic transverse (cyclotron) motion under internal fictitious fluxes. In particular, the magnitudes of the transport coefficients are phenomenologically determined by two basic parameters: the doping concentration and T c , quantitatively consistent with the experimental measurements including the signs and qualitative temperature and magnetic-field dependence. Combined with the predictions of the spinon longitudinal transport properties, including the Nernst and spin Hall effects, a phenomenological description of the pseudogap phase is established as characterized by the neutral spinon excitations, which eventually become “confined” with an intrinsic superconducting transition at T c . Finally, within this theoretical framework, the “order to order” phase transition between the superconducting and antiferromagnetic insulating phases are briefly discussed, with the thermal Hall monotonically increasing into the latter. Published by the American Physical Society 2024
The large thermal Hall conductivity recently detected in Mott insulating cuprates has been attributed to chiral neutral spin excitations. A quantum spin liquid (QSL) with Majorana excitations, Chern number $\ifmmode\pm\else\textpm\fi{}4$ and large thermal Hall conductivity is found to be an excited state of a frustrated Heisenberg model on the square lattice. Using a Majorana mean-field theory and exact diagonalizations, we explore two possible routes to achieve this chiral QSL, an orbital magnetic-field effect and spin-orbit couplings as present in cuprates. In particular, we show how only the orbital magnetic field allows this topological phase to be the ground state, while it remains an excited state of the Majorana mean field under the Dzyaloshinskii-Moriya terms. A large quantized low-temperature thermal Hall effect can be induced in our model of Mott insulating cuprates by the orbital effect of an applied magnetic field.