SciPost Submission Page
Topological phase transition between the gap and the gapless superconductors
by Yuriy Yerin, Caterina Petrillo, A.A.Varlamov
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Yuriy Yerin |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202109_00018v3 (pdf) |
| Date accepted: | 2022-01-06 |
| Date submitted: | 2021-12-28 15:48 |
| Submitted by: | Yerin, Yuriy |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Computational |
Abstract
It is demonstrated that the known for a long time transition between the gap and the gapless states in the Abrikosov-Gor'kov theory of a superconductor with paramagnetic impurities is of the Lifshitz type, i.e. of the $2\frac12$ order phase transition. We reveal the emergence of a cuspidal edge at the density of states surface $N(\omega,\Delta_0)$ ($\Delta_0$ is the value of the superconducting order parameter in the absence of magnetic impurities) and the occurrence of the catastrophe phenomenon at the transition point. We study the stability of such a transition with respect to the spatial fluctuations of the magnetic impurities critical concentration $n_s$ and show that the requirement for validity of its mean field description is unobtrusive: $\nabla \left( {\ln {n_s}} \right) \ll \xi^{-1} $ (here $\xi$ is the superconducting coherence length). Finally, we show that, similarly to the Lifshitz point, the $2\frac12$ order phase transition should be accompanied by the corresponding singularities. For instance, the superconducting thermoelectric effect has a giant peak exceeding the normal value of the Seebeck coefficient by the ratio of the Fermi energy and the superconducting gap. The concept of the experiment for the confirmation of $2\frac12$ order transition nature is proposed. The obtained theoretical results can be applied for the explanation of recent experiments with lightwave-driven gapless superconductivity, for the new interpretation of the disorder induced transition $s_{\pm}$-$s_{++}$ states via gapless state in multi-band superconductors, for better understanding of the gapless color superconductivity in quantum chromodynamics, the string theory.
Author comments upon resubmission
Thank you for giving us another opportunity to improve the manuscript. Following the recommendations of one of the referees, we removed from the paper the mentioning of the possibility of characterization of the gap-gapless transition by means of the topological invariant in the form of the Euler characteristic. Correspondingly, we removed the word “topological” also from the title of the paper.
Concerning the place of publication, we would like to draw your attention to the recommendation of one of the referees that the manuscript is worthy of publication in SciPost. This work has already been presented at several conferences and has attracted lively interest not only from theorists, but also from experimentalists.
Finally, the paper is not only about the Lifshitz nature of the transition in the Abrikosov-Gorkov theory, but also concerns the possible application of the found circumstance to other areas of physics: namely, the change of symmetry of the order parameter in the two-gap superconductor and quantum chromodynamics.
In view of these facts, we hope to see our paper published at the pages SciPost.
Best regards and Happy New Year
Yuriy Yerin
Caterina Petrillo
Andrey Varlamov
List of changes
1. Following the recommendations , we eliminated from the paper the mentioning of the possibility of characterization of the gap-gapless transition by means of of the Euler characteristic.
2. We removed the word “topological” also from the title of the paper and correspondingly we changed the title of the paper.
3. We stressed out on the emergence of the cuspidal edge at the density of states surface $N(\omega,\Delta_0)$ ($\Delta_0$ is the value of the superconducting order parameter in the absence of magnetic impurities) and the occurrence of the catastrophe phenomenon at the transition point.
Published as SciPost Phys. Core 5, 009 (2022)