Intrinsic Thermal Hall Effect in Mott Insulators

The study conducted by Jixun K. Ding, Emily Z. Zhang, Wen O. Wang, Tessa Cookmeyer, Brian Moritz, Yong Baek Kim, and Thomas P. Devereaux delves into the intrinsic thermal Hall effect in Mott insulators. The research was prompted by recent experimental findings that suggested a significant thermal Hall effect in square lattice antiferromagnetic Mott insulators. The primary objective was to determine if a simple Mott insulator could indeed sustain a finite thermal Hall effect. Initially, calculations within a spin-only low-energy effective spin model with non-interacting magnons indicated that the answer was negative. However, through the utilization of determinant quantum Monte Carlo simulations, the researchers were able to demonstrate that the single-band $t$-$t'$-$U$ Hubbard model coupled to an orbital magnetic field could support a finite thermal Hall effect under specific conditions where $t' \neq 0$ and $B \neq 0$ in the Mott insulating phase. The study also highlighted that observing a finite thermal Hall effect necessitates time-reversal and particle-hole symmetry breaking. By analyzing magnon-magnon scattering using a semi-classical Boltzmann approach, the researchers illustrated a physical mechanism through which finite transverse thermal conductivity could arise. These findings challenge conventional beliefs that square and triangular lattices with SU(2) symmetry do not exhibit a finite thermal Hall effect. In conclusion, this research calls for a critical re-examination of thermal Hall effect data in insulating magnets as it emphasizes the importance of considering magnon contributions rather than excluding them outright. The comprehensive analysis presented in this study provides valuable insights into the complex behavior of thermal properties in Mott insulators and opens up new avenues for further exploration in this field of study.

Introduction:

The study conducted by Jixun K. Ding, Emily Z. Zhang, Wen O. Wang, Tessa Cookmeyer, Brian Moritz, Yong Baek Kim, and Thomas P. Devereaux delves into the intrinsic thermal Hall effect in Mott insulators. This research was prompted by recent experimental findings that suggested a significant thermal Hall effect in square lattice antiferromagnetic Mott insulators.

Background:

Mott insulators are materials that do not conduct electricity due to strong electron-electron interactions. They have been extensively studied for their unique properties and potential applications in quantum computing and spintronics. In recent years, there has been growing interest in understanding the thermal properties of these materials.

One important aspect of thermal properties is the thermal Hall effect - a phenomenon where heat flows perpendicular to an applied temperature gradient instead of parallel as expected in conventional materials. This effect has been observed in various systems such as superconductors and topological materials but its existence in Mott insulators has been debated.

Objective:

The primary objective of this study was to determine if a simple Mott insulator could indeed sustain a finite thermal Hall effect. Previous calculations using a spin-only low-energy effective spin model with non-interacting magnons had indicated that this was not possible.

Methodology:

To address this question, the researchers utilized determinant quantum Monte Carlo simulations - a powerful computational technique used to solve complex many-body problems accurately. By simulating the single-band $t$-$t'$-$U$ Hubbard model coupled to an orbital magnetic field under specific conditions where $t' \neq 0$ and $B \neq 0$, they were able to demonstrate that a finite thermal Hall effect can indeed exist in Mott insulators.

Results:

The results showed that observing a finite thermal Hall effect necessitates time-reversal and particle-hole symmetry breaking - two key factors often overlooked when studying thermal properties in Mott insulators. The researchers also analyzed magnon-magnon scattering using a semi-classical Boltzmann approach and proposed a physical mechanism through which finite transverse thermal conductivity could arise.

Implications:

These findings challenge conventional beliefs that square and triangular lattices with SU(2) symmetry do not exhibit a finite thermal Hall effect. This calls for a critical re-examination of thermal Hall effect data in insulating magnets as it emphasizes the importance of considering magnon contributions rather than excluding them outright.

Conclusion:

In conclusion, this research provides valuable insights into the complex behavior of thermal properties in Mott insulators. It highlights the need to consider both time-reversal and particle-hole symmetry breaking when studying these materials and opens up new avenues for further exploration in this field of study. The comprehensive analysis presented in this study has important implications for our understanding of Mott insulators and their potential applications in various fields.