Comment on the paper by D. Efremov and Yu.N. Ovchinnikov "Singular ground state of multiband inhomogeneous superconductors", Phys. Rev. B 99, 224508 (2019)

TL;DR

This paper refutes a previous claim by demonstrating that the earlier conclusion about the absence of spontaneous magnetic fields in multiband superconductors with broken time reversal symmetry is incorrect due to a fundamental inconsistency in the original analysis.

Contribution

The authors identify and correct a flaw in the prior work, showing that the previous conclusion was based on an invalid approximation and providing a proper solution to the Ginzburg-Landau equations.

Findings

The previous claim about no spontaneous magnetic fields is incorrect.

The original analysis neglected a key Ginzburg-Landau equation.

Proper solutions indicate the presence of spontaneous magnetic fields.

Abstract

We show that the conclusion reported in Ref. 1, that there are no spontaneous magnetic fields in multiband superconductors that break time reversal symmetry, is incorrect. We demonstrate that the state proposed in Ref. 1 is not a solution of the Ginzburg-Landau equations for the considered model. The reason is that in Ref. 1 one of the Ginzburg-Landau equations is neglected and substituted by the spurious zero current restriction. This restriction together with all of the Ginzburg-Landau equations leads to an overdetermined system which does not have a solution. This inconsistency invalidates all the results of the paper.