Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Extrinsic contribution to bosonic thermal Hall transport

Léo Mangeolle, Johannes Knolle

TL;DR

The paper develops a gauge-invariant kinetic theory for bosonic thermal Hall transport in the presence of general disorder, deriving a disorder-induced side-jump contribution that can be as large as the intrinsic Berry-curvature term. A central result is the disorder-averaged current, with the extrinsic thermal Hall conductivity given by $\kappa_{xy}^{\rm dis}$, which depends on a disorder-induced curvature $\mathsf\Omega^{\mathsf W}_{p_\mu p_\nu}$ and the detailed impurity matrix structure $\hat{W}$. The authors show that extrinsic effects can shift, enhance, or even invert the total thermal Hall response and provide explicit schemes to compute these contributions in concrete models, including a honeycomb $K\Gamma\Gamma'$ spin model in a magnetic field and a low-energy bosonic field theory. Their results have broad implications for interpreting THE measurements in magnetic insulators, suggesting that both intrinsic and extrinsic mechanisms must be considered to obtain reliable insights into bosonic wavefunctions and topological properties.

Abstract

Bosonic excitations like phonons and magnons dominate the low-temperature transport of magnetic insulators. Similar to electronic Hall responses, the thermal Hall effect (THE) of charge neutral bosons has been proposed as a powerful tool for probing topological properties of their wavefunctions. For example, the intrinsic contribution of the THE of a perfectly clean system is directly governed by the distribution of Berry curvature, and many experiments on topological magnon and phonon insulators have been interpreted in this way. However, disorder is inevitably present in any material and its contribution to the THE has remained poorly understood. Here we develop a rigorous kinetic theory of the extrinsic side-jump contribution to the THE of bosons. We show that the extrinsic THE can be of the same order as the intrinsic one but sensitively depends on the type of local imperfection. We study different types of impurities and show that a THE can even arise as a pure impurity-induced effect in a system with a vanishing intrinsic contribution. As a side product, we also generalize existing results for the electronic AHE to general types of impurities beyond the standard assumption of local potential scattering. We discuss the importance of our results for the correct interpretation of THE measurements.

Extrinsic contribution to bosonic thermal Hall transport

TL;DR

The paper develops a gauge-invariant kinetic theory for bosonic thermal Hall transport in the presence of general disorder, deriving a disorder-induced side-jump contribution that can be as large as the intrinsic Berry-curvature term. A central result is the disorder-averaged current, with the extrinsic thermal Hall conductivity given by , which depends on a disorder-induced curvature and the detailed impurity matrix structure . The authors show that extrinsic effects can shift, enhance, or even invert the total thermal Hall response and provide explicit schemes to compute these contributions in concrete models, including a honeycomb spin model in a magnetic field and a low-energy bosonic field theory. Their results have broad implications for interpreting THE measurements in magnetic insulators, suggesting that both intrinsic and extrinsic mechanisms must be considered to obtain reliable insights into bosonic wavefunctions and topological properties.

Abstract

Bosonic excitations like phonons and magnons dominate the low-temperature transport of magnetic insulators. Similar to electronic Hall responses, the thermal Hall effect (THE) of charge neutral bosons has been proposed as a powerful tool for probing topological properties of their wavefunctions. For example, the intrinsic contribution of the THE of a perfectly clean system is directly governed by the distribution of Berry curvature, and many experiments on topological magnon and phonon insulators have been interpreted in this way. However, disorder is inevitably present in any material and its contribution to the THE has remained poorly understood. Here we develop a rigorous kinetic theory of the extrinsic side-jump contribution to the THE of bosons. We show that the extrinsic THE can be of the same order as the intrinsic one but sensitively depends on the type of local imperfection. We study different types of impurities and show that a THE can even arise as a pure impurity-induced effect in a system with a vanishing intrinsic contribution. As a side product, we also generalize existing results for the electronic AHE to general types of impurities beyond the standard assumption of local potential scattering. We discuss the importance of our results for the correct interpretation of THE measurements.
Paper Structure (57 sections, 150 equations, 3 figures, 2 tables)

This paper contains 57 sections, 150 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Setup
  3. Reminders about the clean case
  4. Introducing disorder
  5. Equal-time formalism
  6. Derivation of the kinetic equation
  7. Phase space formulation and semiclassical approximations
  8. Gauge-invariant coordinates and shift
  9. Corrected kinetic equation: practical implementation and further assumptions
  10. The disorder-induced curvature
  11. The disorder matrix structure $\hat{\sf W}$
  12. Coordinate shift effects in the thermal Hall current
  13. Solving the kinetic equation
  14. The "jump-forward" term
  15. The "side-jump" accumulation term
  16. ...and 42 more sections

Figures (3)

  • Figure 1: Thermal Hall conductivity divided by temperature $\kappa_{xy}/T$ as a function of temperature $T$ for three different instances (a,b,c) of disorder and time reversal (TR) breaking parameters, in a minimal model of bosons with viscosity (TR-breaking) terms introduced in Sec. \ref{['sec:applications']}. $\kappa_{xy}^{\rm clean}$ is the intrinsic contribution in the absence of disorder (Eq.\ref{['eq:31']}), $\kappa_{xy}^{\rm dis}$ is the contribution due to disorder (Eq.\ref{['eq:32']}), and $\kappa_{xy}^{\rm tot}=\kappa_{xy}^{\rm clean}+\kappa_{xy}^{\rm dis}$. Both axes are in arbitrary units, identical in all three plots. (a) Disorder is a local modulation of the clean Hamiltonian, with identical matrix structure. (b) Disorder is a local viscosity term, distinct from that already present in the clean theory. (c) The clean theory has zero viscosity and preserves TR, but impurities still introduce TR breaking locally: remarkably, in this case thermal Hall conductivity is a pure impurity effect. (a,b,c) The temperature dependences and distinctive features of these curves are discussed in Sec.\ref{['sec:discussion']}.
  • Figure 2: Graphical representation of our equal-time procedure, inspired by rammerbook. The horizontal direction represents time (with later times to the left), and the dashed lines represent a statistical contraction as per Eq.\ref{['eq:8']}. Symbols are defined in the first line, and the other three lines represent Eqs.\ref{['eq:10']}-\ref{['eq:11']}, Eq.\ref{['eq:12']} and Eq.\ref{['eq:13']}, respectively. We use the shorthand $D_t \mathsf F_{\rm d} = \partial_t +i [{\sf K}_{\rm d}\,\overset{\circ},\,{\sf F}_{\rm d}]$, and for notational clarity $\hbar=1$.
  • Figure 3: Thermal Hall conductivity of magnons in the disordered $K\Gamma\Gamma'$ model. Blue, red and yellow curves represent the intrinsic, extrinsic and total contribution, respectively. Different symbols account for different instances of disorder (for instance filled disks mean $K$-type disorder). Right axis: experimental quantity $\kappa_{xy}^{3D}/T$ in SI units. Left axis: equivalent 2D quantity $\kappa_{xy}^{2D}/T$ in units of the thermal Hall quantum.