Invalidity of Classes of Approximated Hall Effect Calculations

TL;DR

This paper critiques certain approximated derivations of the effective equation of motion in d-wave superconductors, highlighting that the relaxation time approximation used is invalid and unnecessary.

Contribution

It identifies the invalidity of the relaxation time approximation in specific derivations related to d-wave superconductors.

Findings

The relaxation time approximation is inappropriate for these calculations.

The approximations previously used are fundamentally flawed.

Correct derivations do not require the relaxation time approximation.

Abstract

In this comment, I point out a number of approximated derivations for the effective equation of motion, now been applied to d-wave superconductors by Kopnin and Volovik are invalid. The major error in those approximated derivations is the inappropriate use of the relaxation time approximation in force-force correlation functions, or in force balance equations, or in similar variations. This approximation is wrong and unnecessary.