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

TL;DR

This study measures the electronic thermal resistivity in bismuth, revealing a T-square temperature dependence with a prefactor related to the Fermi temperature, providing insights into fermion-fermion collision cross-sections in semi-metals.

Contribution

The paper presents high-resolution thermal conductivity measurements in bismuth, linking the T-square resistivity prefactor to Fermi temperature and fermion collision cross-sections, which was not previously established.

Findings

Electronic thermal resistivity follows T-square dependence.

Prefactor of thermal resistivity scales with inverse Fermi temperature.

Fermion-fermion collision cross-section is proportional to Fermi wavelength.

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 $\hbar/k_FE_F^2$. 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.