Thermal transport in compensated semimetals: Effect of electron-electron scattering on Lorenz ratio

Abstract

It is well known that the electronic thermal conductivity of clean compensated semimetals can be greatly enhanced over the electric conductivity by the availability of an ambipolar mechanism of conduction, whereby electrons and holes flow in the same direction experiencing negligible Coulomb scattering as well as negligible impurity scattering. This enhancement -- resulting in a breakdown of the Wiedemann-Franz law with an anomalously large Lorenz ratio -- has been recently observed in two-dimensional monolayer and bilayer graphene near the charge neutrality point. In contrast to this, three-dimensional compensated semimetals such as WP$_2$ and Sb are typically found to show a reduced Lorenz ratio. This dramatic difference in behavior is generally attributed to different regimes of Fermi statistics in the two cases: degenerate electron-hole liquid in compensated semimetals versus non-degenerate electron-hole liquid in graphene. We show that this difference is not sufficient to explain the reduction of the Lorenz ratio in compensated semimetals. We argue that the solution of the puzzle lies in the ability of compensated semimetals to sustain sizeable regions of electron-hole accumulation near the contacts, which in turn is a consequence of the large separation of electron and hole pockets in momentum space. These accumulations suppress the ambipolar conduction mechanism and effectively split the system into two independent electron and hole conductors. We present a quantitative theory of the crossover from ambipolar to unipolar conduction as a function of the size of the electron-hole accumulation regions, and show that it naturally leads to a sample-size-dependent thermal conductivity.