Microscopic origin of an exceptionally large phonon thermal Hall effect from charge puddles in a topological insulator

TL;DR

This study addresses the origin of an unusually large phonon-dominated thermal Hall effect in the compensated topological insulator TlBi$_{0.15}$Sb$_{0.85}$Te$_2$. It combines transport measurements showing a sizable $\kappa_{xy}/\kappa_{xx} \approx 0.02$ in moderate magnetic fields with a two-temperature theoretical framework in which dilute charged impurities create charge puddles that couple to phonons and imprint a transverse heat flow. The key finding is that the field-dependent heating of puddles, described by a diffusion/Poisson-like model, yields a nonmonotonic $\kappa_{xy}(B)$ scaling approximately as $\frac{e\mu n}{1+\mu^2B^2}$ and that the observed giant THE arises from the collective contribution of these puddles to the phonon system, not from electronic heat transport. This work links microscopic impurity-induced inhomogeneity and large dielectric screening to a robust route for engineering large phonon THE in insulating materials, with potential implications for thermal management and phononics in quantum materials.

Abstract

We present the experimental observation of a drastically enhanced thermal Hall effect in the topological insulator material TlBi$_{0.15}$Sb$_{0.85}$Te$_2$. Although heat transport is dominated by phonons, moderate magnetic fields generate a thermal Hall ratio ($κ_{xy}/κ_{xx}$) above 2\%, an unprecedented value for a nonmagnetic material. The transverse thermal conductivity $κ_{xy}$ exhibits a pronounced maximum in fields of a few Tesla. This characteristic field dependence allows us to identify the microscopic origin of the thermal Hall effect in this system. Small densities of charged impurities induce locally conducting regions, so-called charge puddles, within the bulk insulating matrix. Via electron-phonon coupling, these charge puddles imprint a large thermal Hall effect onto the phonons accounting for both the magnitude and the magnetic-field dependence of the observed effect.

Figures (10)

• Figure 1: (a) Spatially varying energy spectrum in a compensated TI containing charged impurities ShklovskiiEfros1972PhysRevLett.109.176801. The lines represent the conduction and valence band edges, E$_C$ and E$_V$, respectively, and the shaded areas indicate the formation of electron- or hole-type charge puddles in regions where the chemical potential $\mu$ crosses either E$_C$ or E$_V$. (b) Schematic setup to measure the longitudinal and transverse temperature differences ($\Delta\textrm{T}_\textrm{x} = T_1-T_2$, $\Delta\textrm{T}_\textrm{y} = T_2-T_3$). A longitudinal heat current from the heater to the heat bath is mainly carried by phonons inducing temperature gradients in electron and hole puddles. Due to the electronic $\kappa^{ch}_{xy}$, the puddles develop a temperature gradient in perpendicular direction (indicated by $+$ and $-$ in the red and blue dots), heating the phonons. This results in a transversal temperature gradient of the phonon system dominantly from hole puddles (see text).
• Figure 2: (a) Electrical conductivities $\rho_{xx}$ and (b) thermal conductivities $\kappa_{xx}$ of TlBi$_{0.15}$Sb$_{0.85}$Te$_2$ samples S1 and S2. In (b), we also show the estimated contribution $\sigma_{xx}L_0T$ from mobile charge carriers based on the Wiedemann-Franz law for the better conducting sample S2. (c,d) Thermal Hall conductivities $\kappa_{xy}$ of both samples for different magnetic fields, which strongly exceed the estimated charge-carrier contributions $\sigma_{xy}L_0T$ based on the electrical Hall conductivities.
• Figure 3: Hall ratios $\kappa_{xy}/\kappa_{xx}$ of TlBi$_{0.15}$Sb$_{0.85}$Te$_2$ samples S1 and S2 are drastically enhanced to about 2 % at moderate magnetic fields from about 2 to $8\,$T over a wide temperature range of more than 100 K.
• Figure 4: (a,b) Field dependent thermal Hall conductivity $\kappa_{xy}$ of TlBi$_{0.15}$Sb$_{0.85}$Te$_2$ samples converted to electrical Hall conductivity units by using Wiedemann-Franz law. Dashed lines are fits of a single-band model of hole-like charge carriers, see Eq. \ref{['eq:Hall1']}. (c,d) Temperature dependent fit parameters of the obtained hole-like carrier densities $n(T)$ and their mobilities $\mu(T)$ for both samples S1 and S2.
• Figure 5: Heat maps of charge-carrier temperature $T^{ch}({\boldsymbol r})$ computed from Eq. \ref{['eq:heat_coupled']} for spherical hole-doped puddles of different sizes and a phonon heat current in the $+x$ direction (arrow). Parameters: $\mu B=2$, $R_\text{eff}=1,2,3,4$, only the lower half of the puddle, $z<0$ is shown. The Hall effect leads to an asymmetric heating and cooling. Larger puddles equilibrate better with the phonons. The color scale (see legend) is chosen such that $1$ and $-1$ corresponds to the phonon temperatures at the beginning and end of each puddle.