Thermal Hall conductivity of semi-metallic graphite dominated by ambipolar phonon drag

TL;DR

Graphite, a compensated semimetal with high-mobility electrons and holes and highly conductive phonons, exhibits a thermal Hall response κ_xy that far exceeds the electronic contribution predicted by the Wiedemann–Franz law, yielding a Hall Lorenz number around 67 L0. By combining measurements of κ_xy, κ_xx, α_xy, S_xx, S_xy and a two-band analysis of σ_xy, the study identifies ambipolar phonon drag as the dominant mechanism generating the large, sign-changing κ_xy; this drag is quantified through a field- and temperature-dependent phonon-drag Seebeck coefficient S_drag ≈ -60 μV/K at 28 K. The phase relation between α_xy and κ_xy supports a drag-mediated transfer of momentum between phonons and the electron-hole reservoir. These results show that giant thermal Hall responses are achievable in metals with high-velocity phonons and coexisting electron and hole carriers, challenging the universality of the Wiedemann–Franz law in multi-carrier, phonon-dominated regimes.

Abstract

It is now known that in addition to electrons, other quasi-particles such as phonons and magnons can also generate a thermal Hall signal. Graphite is a semimetal with extremely mobile charge carriers of both signs and a large lattice thermal conductivity. We present a study of the thermal Hall effect in highly oriented pyrolytic graphite (HOPG) samples with electronic, phononic and phonon drag contributions to the thermal Hall signal. The measured thermal Hall conductivity ($κ_{xy}$) is two orders of magnitude higher than what is expected by electronic carriers according to the electrical Hall conductivity and the Wiedemann-Franz law, yielding a record Hall Lorenz number of $164.9\times10^{-8}V^2 K^{-2}$ ($\sim$67$L_0$) - the largest ever observed in a metal. The temperature dependence of the thermal Hall conductivity significantly differs from its longitudinal counterpart, ruling out a purely phononic origin of the non-electronic component. Based on the temperature dependence and the amplitudes of the Seebeck and Nernst responses, we demonstrate that ambipolar phonon drag dominates the thermal Hall response of graphite.

Figures (15)

• Figure 1: Brillouin zone, experimental setup, longitudinal transport properties, and electric/thermal Hall conductivity in graphite. (a) The Brillouin zone, electron and hole Fermi pockets in graphite. (b) Experimental configuration for measurement of longitudinal/transverse electric, thermoelectric, and thermal transport. (c) Temperature-dependent longitudinal resistivity ($\rho_{xx}$) and Seebeck coefficient ($S_{xx}$), showing a phonon drag peak near 30 K in $S_{xx}$. (d) Temperature dependence of longitudinal thermal conductivity ($\kappa_{xx}$). The dashed curve indicates negligible electronic contribution ($\kappa_{xx}^e$) estimated via $L_0\sigma_{xx}T$. (e) Field dependence of electric Hall conductivity ($\sigma_{xy}$) at 28.2 K (low temperature) and 302.5 K (room temperature), exhibiting sharp peaks. (f) Field-dependent thermal Hall conductivity ($\kappa_{xy}$) at 28.2 K and 302.5 K, showing gentler peaks with sign reversal between temperatures. Additional data points are provided in Supplementary Materials SM.
• Figure 2: Comparison of $\kappa_{xx}$, $\kappa_{xy}$ and $L_0\sigma_{xy}T$. (a-b) Measured thermal Hall conductivity $\kappa_{xy}$ versus the theoretically expected electronic contribution $\kappa_{xy}^e = L_0\sigma_{xy}T$. The experimental values exceed the theoretical predictions by two orders of magnitude at 28.2 K and by a factor of five at 302.5 K, indicating a significant enhancement mechanism beyond electronic contributions. (c-d) Hall conductivity curves fit to a two-band model ($\sigma_H(B) = \frac{ne\mu_e^2B}{1+\mu_e^2B^2} - \frac{pe\mu_h^2B}{1+\mu_h^2B^2}$). (e) Temperature-dependence of $\kappa_{xx}$, $\kappa_{xy}$ and $L_0\sigma_{xy}T$. Also shown are carrier mobilities ($\mu_e$ and $\mu_h$). The contrasting trends between $\kappa_{xy}$ and $\kappa_{xx}$ suggest distinct physical origins for these transport phenomena.
• Figure 3: Transverse ambipolar phonon drag. (a) Schematic of thermal Hall phonon drag in compensated systems. Momentum-conserving collisions between carriers and phonons generate a transverse temperature gradient. The transverse electronic current ($J^e_y = \alpha_{xy} \nabla T_x$) induces transverse phonon momentum flow, resulting in phonon heat flow (($J^Q_y = \Pi_{drag} J^e_y$)). (b) Field dependence of Nernst signal ($S_{xy}$). (c-d) Field and temperature dependence of Nernst conductivity ($\alpha_{xy}$), extracted from $S_{xy}$, $S_{xx}$, $\rho_{xy}$, $\rho_{xx}$ (see Supplementary Materials SM for details). (e) Extracted temperature-dependent phonon drag Seebeck coefficient $S_{drag} = (\kappa_{xy} - L_0\sigma_{xy}T) / (\alpha_{xy} T)$, compared to the measured Seebeck signal under field of 0.5 T (low temperature) and 3 T (high temperature). At 28.2 K, it reaches -60 $\mu$V/K, consistent with the peak measured in Figure \ref{['fig:THE']}c.
• Figure S1: Two sets of transverse temperature difference.
• Figure S2: Thermal Hall angle. Field dependence of thermal Hall angle at eight characteristic temperatures ranging from 28.2 K to 302.5 K.