A Diagrammer's Note on Superconducting Fluctuation Transport for Beginners: Supplement. Boltzmann Equation and Fermi-Liquid Theory

TL;DR

This paper explains how the Boltzmann equation and Fermi-liquid theory relate in superconducting fluctuation transport, emphasizing collision terms, electron interactions, and geometrical factors, with insights into Hall conductivity calculations.

Contribution

It clarifies the consistency between Boltzmann and Fermi-liquid theories in superconducting fluctuations, including collision effects and geometrical considerations, and discusses limitations of the FLEX approximation.

Findings

Confirmed the consistency between Boltzmann and Fermi-liquid theories.

Analyzed the collision term effects on conductivity.

Discussed geometrical factors and the Tsuji formula for Hall conductivity.

Abstract

The effect of the collision term of the Boltzmann equation is discussed for the diagonal conductivity in the absence of magnetic field and the off-diagonal conductivity within the linear order of magnetic field. The consistency between the Boltzmann equation and the Fermi-liquid theory is confirmed. The electron-electron interaction is totally taken into account via the self-energy of the electron. The Umklappness is taken into account as the geometrical factor. The current-vertex correction in the fluctuation-exchange (FLEX) approximation violates these conventional schemes. In the Appendix the Tsuji formula, the geometrical formula for the Hall conductivity is discussed.