Critical fields of superconductors with magnetic impurities

Journal Article · 03 August 2022 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.106.054505 · OSTI ID:1881869

Kogan, V. G.  ^[1]; Prozorov, R.  ^[1]

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1. Ames Lab., Ames, IA (United States); Iowa State Univ., Ames, IA (United States)

The upper critical field H_c2, the field H_c3 for nucleation of the surface superconductivity, and the thermodynamic field H_c 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 $$\mathscr{R}$$=H_c3/H_c2 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 F_c and the thermodynamic critical field H_c for any temperature and scattering parameters. By comparing H_c2 and H_c, we find that, unlike transport scattering, the pair-breaking pushes materials toward type-I behavior. Furthermore, we find a peculiar behavior of F_c 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.

• Research Organization: Ames Laboratory (AMES), Ames, IA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
• Grant/Contract Number: AC02-07CH11358; AC02-07CH11359
• OSTI ID: 1881869
• Report Number(s): IS-J 10,870
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 5 Vol. 106; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English