Thermal Hall conductivity of semimetallic graphite dominated by ambipolar phonon drag

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.

💡 Research Summary

In this work the authors present the first comprehensive study of the thermal Hall effect in highly oriented pyrolytic graphite (HOPG), a compensated semimetal with exceptionally mobile electrons and holes and a dominant phonon heat conduction channel. By simultaneously measuring longitudinal resistivity (ρxx), Seebeck coefficient (Sxx), longitudinal thermal conductivity (κxx), electric Hall conductivity (σxy), Nernst coefficient (Sxy) and the transverse thermal conductivity (κxy) over a temperature range of 20 K to 300 K and magnetic fields up to 1 T, they uncover several striking phenomena.

First, κxy reaches –819 mW K⁻¹ m⁻¹ at 28 K (0.25 T) and +3.3 W K⁻¹ m⁻¹ at 300 K (1 T), values that exceed the electronic contribution predicted by the Wiedemann‑Franz law (κe = L0 σxy T) by two orders of magnitude at low temperature and by a factor of five at room temperature. Consequently the Hall Lorenz number Lxy = κxy/(σxy T) attains 164.9 × 10⁻⁸ V² K⁻², i.e. about 67 L0, the largest ever reported for any metal.

Second, κxy changes sign near 100 K: it is negative at low temperature and becomes positive at higher temperature, while the longitudinal thermal conductivity κxx shows a conventional phonon‑dominated peak around 30 K and never changes sign. The distinct temperature dependences of κxy and κxx rule out a purely phononic origin of the transverse heat current.

Third, detailed analysis of the electric Hall response using a two‑band model yields temperature‑dependent electron and hole mobilities (μe ≈ 2.7 × 10⁴ cm² V⁻¹ s⁻¹, μh ≈ 2.5 × 10⁴ cm² V⁻¹ s⁻¹ at low temperature) and confirms that the Hall conductivity σxy remains positive across the whole temperature range, reflecting the higher electron mobility.

The authors then invoke the concept of ambipolar phonon drag. Building on Herring’s theory, they argue that a longitudinal temperature gradient generates a transverse electric current via the Nernst conductivity (αxy), which in turn drags phonons and produces a transverse heat current. This leads to the relation κdrag = Πdrag αxy = Sdrag T αxy. By extracting αxy from the measured Nernst signal and comparing its magnetic‑field profile with that of κxy, they find an almost perfect match. Using the peak values they calculate a phonon‑drag Seebeck coefficient Sdrag of –60 µV K⁻¹ at 28 K, consistent with the independent Seebeck peak observed in Sxx.

Importantly, the sign of Sdrag switches from negative at low temperature (electron‑dominated drag) to positive at higher temperature (hole‑dominated drag). This temperature‑dependent crossover explains the sign reversal of κxy: at low T the electron‑phonon momentum exchange yields a negative transverse heat flow, while at high T the hole‑phonon exchange produces a positive flow. Around 100 K the contributions from electrons and holes nearly cancel, leading to the observed near‑zero κxy.

A comparative table shows that the Hall Lorenz number of graphite far exceeds that of other metals and correlated oxides (Cu, YBa₂Cu₃O₆, SrTiO₃‑δ, FeSn, Mn₃Sn, etc.), highlighting graphite as a unique platform where the Wiedemann‑Franz law is dramatically violated. The authors conclude that the combination of (i) a huge phonon thermal conductivity, (ii) high‑mobility ambipolar charge carriers, and (iii) strong electron‑hole–phonon momentum exchange produces an unprecedented thermal Hall response. This work not only identifies ambipolar phonon drag as a dominant mechanism in a compensated metal but also opens new avenues for exploiting phonon‑drag‑enhanced transverse heat transport in thermoelectric and spin‑caloritronic applications. Future ab‑initio calculations and extended experimental regimes are suggested to quantitatively model the electron‑hole–phonon coupling that underlies the observed phenomena.