Comment on "Fluctuation-induced first-order transition p-wave superconductors" by Qi Li, D. Belitz, and J. Toner [Phys. Rev. B79, 054514 (2009)]

TL;DR

This paper critiques a previous study on p-wave superconductors, correcting the mean-field analysis, identifying missing phases, and discussing shortcomings in prior theoretical approaches.

Contribution

It provides a corrected mean-field analysis of the model, revealing a stable non-unitary phase and highlighting errors and limitations in earlier work.

Findings

Identification of a stable non-unitary phase

Correction of the mean-field analysis

Discussion of errors in prior studies

Abstract

In this Comment, we show that the paper by Qi Li, D. Belitz and J. Toner, published in Phys. Rev. B {\bf 79}, 054514 (2009), contains an incomplete mean-field analysis of a simple model of Ginzburg-Landau type. The latter contains a stable non-unitary phase, which has not been found in this study and is missing in the outlined picture of possible stable phases. In this Comment, the mean field analysis has been corrected, the errors have been explained in details and relevant topics have been discussed. Shortcomings in the mean-field-like and renormalization group studies in the mentioned paper have also been revealed.