Intrinsic Nonlinear Planar Thermal Hall Effect

Abstract

We introduce the intrinsic nonlinear planar thermal Hall effect (NPTHE)-- a dissipationless thermal response proportional to $(\nabla T)^2B$, which arises when the temperature gradient $\nabla T$ and magnetic field $\mathbf{B}$ lie within the same plane. The effect originates from a thermal gradient induced correction to the Berry curvature, characterized by the thermal Berry connection polarizability (TBCP) tensor, leading to a nonlinear transverse heat current independent of scattering time. A symmetry analysis shows that the intrinsic NPTHE is permitted only in noncentrosymmetric crystal point groups lacking horizontal mirror symmetry. Using a tilted Dirac model, we demonstrate that its characteristic angular dependence provides an effective means to control the nonlinear thermal response. Our results establish a new class of quantum geometry driven intrinsic nonlinear thermal transport, offering both a sensitive probe of band geometry and a pathway toward nonlinear thermal functionalities in quantum materials.

Figures (1)

• Figure 1: (a) Schematic illustration of the planar thermal Hall geometry, where the temperature gradient $\boldsymbol{\nabla}T$ and magnetic field $\mathbf{B}$ lie in the same plane, forming polar angles $\theta$ and $\phi$ with respect to the $x$-axis. (b) Angular dependence of the intrinsic nonlinear planar thermal Hall coefficient $\kappa_{H}^{\text{int}}(\theta=\pi/2,\phi)$, shown in units of $\frac{\mathrm{k}_B^2\mu_B}{\hbar}\mathrm{\AA \,eV^{-1}}$, calculated for the tilted 2D Dirac model with different anisotropy ratios: $v_y=v_x$ (red), $v_y=0.7v_x$ (blue), and $v_y=1.5v_x$ (green). (c) Same as (b), but for $\theta=0$. The parameters used are $v_x = 1\times10^6~\mathrm{m/s} \equiv 6.582~\mathrm{eV\AA}$, $m=0.02~\mathrm{eV}$, $t=0.1v_x$, and $\mu=0.05~\mathrm{eV}$.