Electronic thermal resistivity and quasi-particle collision cross-section in semi-metals

Abstract

Electron-electron collisions lead to a T-square component in the electrical resistivity of Fermi liquids. The case of liquid ${}^3$He illustrates that the \textit{thermal} resitivity of a Fermi liquid has a T-square term, expressed in m$\cdot$W${}^{-1}$. Its natural units are $\hslash /k_F{E}_F^2$. Here, we present a high-resolution study of the thermal conductivity in bismuth, employing magnetic field to extract the tiny electronic component of the total thermal conductivity and resolving signals as small as $\approx 60\mu$K. We find that the electronic thermal resistivity follows a T-square temperature dependence with a prefactor twice larger than the electric T-square prefactor. Adding this information to what has been known for other semi-metals, we find that the prefactor of the T-square thermal resistivity scales with the square of the inverse of the Fermi temperature, implying that the dimensionless fermion-fermion collision cross-section is roughly proportional to the Fermi wavelength, indicating that it is not simply set by the strength of the Coulomb interaction.

arXiv comment9 pages, 5 figures

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Cited by in corpus (4)

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• Lorenz ratios of diagonal and Hall conductivities in a Dirac electron liquid
• T-square electric resistivity and its thermal counterpart in RuO${}_2$
• Electron-electron and electron-phonon collision cross sections in CsV3Sb5