Critical fields of superconductors with magnetic impurities
Abstract
The upper critical field Hc2, the field Hc3 for nucleation of the surface superconductivity, and the thermodynamic field Hc are evaluated within the weak-coupling theory for the isotropic s-wave case with arbitrary transport, and pair-breaking scattering. In this study, we find that, for the standard geometry of a half-space sample in a magnetic field parallel to the surface, the ratio $$\mathscr{R}$$=Hc3/Hc2 is within the window 1.55≲$$\mathscr{R}$$≲2.34 , regardless of temperature or the scattering type. While the nonmagnetic impurities tend to flatten the $$\mathscr{R}$$($$\mathrm{T}$$) variation, magnetic scattering merely shifts the maximum of $$\mathscr{R}$$($$\mathrm{T}$$) to lower temperatures. Surprisingly, while reducing the transition temperature, magnetic scattering has a milder impact on $$\mathscr{R}$$ than nonmagnetic scattering. The surface superconductivity is quite robust; in fact, the ratio $$\mathscr{R}$$≈1.7 even in the gapless state. We used Eilenberger's energy functional to evaluate the condensation energy Fc and the thermodynamic critical field Hc for any temperature and scattering parameters. By comparing Hc2 and Hc, we find that, unlike transport scattering, the pair-breaking pushes materials toward type-I behavior. Furthermore, we find a peculiar behavior of Fc as a function of the pair-breaking scattering parameter at the low-$$\mathrm{T}$$ transition from gapped to gapless phases, which has recently been associated with the topological transition in the superconducting density of states.
- Authors:
-
- Ames Lab., Ames, IA (United States); Iowa State Univ., Ames, IA (United States)
- Publication Date:
- Research Org.:
- Ames Laboratory (AMES), Ames, IA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1881869
- Report Number(s):
- IS-J 10,870
Journal ID: ISSN 2469-9950; TRN: US2307872
- Grant/Contract Number:
- AC02-07CH11358; AC02-07CH11359
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 106; Journal Issue: 5; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; critical field; impurities in superconductors; superconducting phase transition; superconductors
Citation Formats
Kogan, V. G., and Prozorov, R. Critical fields of superconductors with magnetic impurities. United States: N. p., 2022.
Web. doi:10.1103/physrevb.106.054505.
Kogan, V. G., & Prozorov, R. Critical fields of superconductors with magnetic impurities. United States. https://doi.org/10.1103/physrevb.106.054505
Kogan, V. G., and Prozorov, R. Thu .
"Critical fields of superconductors with magnetic impurities". United States. https://doi.org/10.1103/physrevb.106.054505. https://www.osti.gov/servlets/purl/1881869.
@article{osti_1881869,
title = {Critical fields of superconductors with magnetic impurities},
author = {Kogan, V. G. and Prozorov, R.},
abstractNote = {The upper critical field Hc2, the field Hc3 for nucleation of the surface superconductivity, and the thermodynamic field Hc are evaluated within the weak-coupling theory for the isotropic s-wave case with arbitrary transport, and pair-breaking scattering. In this study, we find that, for the standard geometry of a half-space sample in a magnetic field parallel to the surface, the ratio $\mathscr{R}$=Hc3/Hc2 is within the window 1.55≲$\mathscr{R}$≲2.34 , regardless of temperature or the scattering type. While the nonmagnetic impurities tend to flatten the $\mathscr{R}$($\mathrm{T}$) variation, magnetic scattering merely shifts the maximum of $\mathscr{R}$($\mathrm{T}$) to lower temperatures. Surprisingly, while reducing the transition temperature, magnetic scattering has a milder impact on $\mathscr{R}$ than nonmagnetic scattering. The surface superconductivity is quite robust; in fact, the ratio $\mathscr{R}$≈1.7 even in the gapless state. We used Eilenberger's energy functional to evaluate the condensation energy Fc and the thermodynamic critical field Hc for any temperature and scattering parameters. By comparing Hc2 and Hc, we find that, unlike transport scattering, the pair-breaking pushes materials toward type-I behavior. Furthermore, we find a peculiar behavior of Fc as a function of the pair-breaking scattering parameter at the low-$\mathrm{T}$ transition from gapped to gapless phases, which has recently been associated with the topological transition in the superconducting density of states.},
doi = {10.1103/physrevb.106.054505},
journal = {Physical Review. B},
number = 5,
volume = 106,
place = {United States},
year = {Thu Aug 04 00:00:00 EDT 2022},
month = {Thu Aug 04 00:00:00 EDT 2022}
}
Works referenced in this record:
Effect of inhomogeneous surface disorder on the superheating field of superconducting RF cavities
journal, August 2019
- Ngampruetikorn, Vudtiwat; Sauls, J. A.
- Physical Review Research, Vol. 1, Issue 1
Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1 ms
journal, September 2012
- Rigetti, Chad; Gambetta, Jay M.; Poletto, Stefano
- Physical Review B, Vol. 86, Issue 10
Nucleation of superconductivity in finite anisotropic superconductors and the evolution of surface superconductivity toward the bulk mixed state
journal, February 2002
- Kogan, V. G.; Clem, J. R.; Deang, J. M.
- Physical Review B, Vol. 65, Issue 9
Onset of surface superconductivity beyond the Saint-James–de Gennes limit
journal, September 2017
- Xie, Hong-Yi; Kogan, Vladimir G.; Khodas, Maxim
- Physical Review B, Vol. 96, Issue 10
Transformation of Gorkov's equation for type II superconductors into transport-like equations
journal, April 1968
- Eilenberger, Gert
- Zeitschrift für Physik A Hadrons and nuclei, Vol. 214, Issue 2
Superconducting Radio-Frequency Fundamentals for Particle Accelerators
journal, January 2012
- Gurevich, Alex
- Reviews of Accelerator Science and Technology, Vol. 05
Normal part of ( H , T ) phase diagram of a superconductor: Possible applications to proximity systems
journal, July 1985
- Kogan, V. G.
- Physical Review B, Vol. 32, Issue 1
Theory of the Thermal Conductivity of Superconducting Alloys with Paramagnetic Impurities
journal, February 1965
- Ambegaokar, Vinay; Griffin, Allan
- Physical Review, Vol. 137, Issue 4A
Changing the type of superconductivity by magnetic and potential scattering
journal, November 2014
- Kogan, V. G.; Prozorov, R.
- Physical Review B, Vol. 90, Issue 18
Experimental Evidence for a new Superconducting Phase Nucleation Field in Type-II Superconductors
journal, February 1964
- Tomasch, W. J.; Joseph, A. S.
- Physical Review Letters, Vol. 12, Issue 6
Topological nature of the transition between the gap and the gapless superconducting states
journal, April 2022
- Yerin, Yuriy; Varlamov, A. A.; Petrillo, Caterina
- Europhysics Letters, Vol. 138, Issue 1
Superconducting Tunneling at High Magnetic Fields and Possible Evidence for Ginzburg Surface Superconductivity
journal, March 1965
- Strongin, Myron; Paskin, Arthur; Kammerer, O. F.
- Physical Review Letters, Vol. 14, Issue 10
Onset of superconductivity in decreasing fields
journal, December 1963
- Saint-James, D.; Gennes, P. G.
- Physics Letters, Vol. 7, Issue 5
Orbital upper critical field of type-II superconductors with pair breaking
journal, July 2013
- Kogan, V. G.; Prozorov, R.
- Physical Review B, Vol. 88, Issue 2
Superconducting Circuits for Quantum Information: An Outlook
journal, March 2013
- Devoret, M. H.; Schoelkopf, R. J.
- Science, Vol. 339, Issue 6124
Resistive Transitions and Surface effects in Type-II Superconductors
journal, February 1964
- Hempstead, C. F.; Kim, Y. B.
- Physical Review Letters, Vol. 12, Issue 6
Temperature and Purity Dependence of the Superconducting Critical Field, . II
journal, July 1966
- Helfand, E.; Werthamer, N. R.
- Physical Review, Vol. 147, Issue 1
London penetration depth and pair breaking
journal, December 2013
- Kogan, V. G.; Prozorov, R.; Mishra, V.
- Physical Review B, Vol. 88, Issue 22
Theoretical estimates of maximum fields in superconducting resonant radio frequency cavities: stability theory, disorder, and laminates
journal, January 2017
- Liarte, Danilo B.; Posen, Sam; Transtrum, Mark K.
- Superconductor Science and Technology, Vol. 30, Issue 3
Critical-temperature enhancement in thin superconducting films due to field dependence of the coherence length
journal, February 1987
- Kogan, Vladimir G.; Nakagawa, Norio
- Physical Review B, Vol. 35, Issue 4
Unusual evolution of Bc2 and Tc with inclined fields in restacked TaS2 nanosheets
journal, July 2018
- Ma, Yonghui; Pan, Jie; Guo, Chenguang
- npj Quantum Materials, Vol. 3, Issue 1
Topological phase transition between the gap and the gapless superconductors
journal, February 2022
- Yerin, Yuriy; Petrillo, Caterina; Varlamov, A. A.
- SciPost Physics Core, Vol. 5, Issue 1
Enhancement of superconductivity by a parallel magnetic field in two-dimensional superconductors
journal, August 2011
- Jeffrey Gardner, H.; Kumar, Ashwani; Yu, Liuqi
- Nature Physics, Vol. 7, Issue 11