Fe-based superconductors: role of the magnetic impurities Maxim M. Korshunov L.V. Kirensky Institute of Physics, Krasnoyarsk, Russia In collaboration with • Oleg Dolgov (MPI FKF Stuttgart) • Alexander Golubov (University of Twente) • Dima Efremov (IFW Dresden) [ICTP EXS-October-2014]
Effect of impurity scattering: single-gap 𝑡 -wave system nonmagnetic impurity Singlet cooper pair magnetic impurity
Fe-based superconductors h A.A. Kordyuk, Low Temp. DFT result: Phys. (2012) Fe 2+ 3d 6 -states Γ e form the FS M Weak CEF splitting: all 5 orbitals (d x2-y2 , d 3z2-r2 , d xy , d xz +d yz ) are near the Fermi level 𝑡 ++ 𝑡 ± nodal 𝑡 ± 𝑒 Symmetry proposals for FeBS “Realistic” Spin Orbital fluctuations, Spin fluctuations Mott-Hubbard-type Phonons fluctuations theories P.J. Hirschfeld, MMK, and I.I. Mazin, Rep. Prog. Phys. 74, 124508 (2011)
Inter- and intraband nonmagnetic impurity scattering in the 2-band 𝑡 ± system k’ -k k k’ mixes + and – Inter- gaps, breaks pairs 𝑣 - D 1 D 2 + k’ -k k’ k Intra- no mixing of +/- k no pairbreaking 𝑤 k’ k’ -k - D 1 D 2 + A.A. Golubov and I.I. Mazin, PRB 55, 15146 (1997), Physica C 243, 153 (1995) P.J. Hirschfeld, MMK, and I.I. Mazin, Rep. Prog. Phys. 74, 124508 (2011)
Non-magnetic vs. magnetic impurities No effect of disorder! Ba 0.5 K 0.5 Fe 2 As 2 Theory: suppression of T c by For Zn (non-magnetic impurity) the non-magnetic impurities suppression of T c is negligible S. Onari, H. Kontani, PRL 103, 177001 (2009) Magnetic impurities (Mn) suppress T c , Δ𝑈 𝑑 (1%Mn) = −4.2K P. Cheng et al., PRB 81, 174529 (2010)
Non-magnetic impurities in a two-band 𝑡 ± state: universal scattering rate Interband and intraband impurities 𝑤 2 = 𝑣 2 𝜃 Impurity strength 𝜌 2 𝑂 𝑏 𝑂 𝑐 𝑣 2 𝜏 = 1 + 𝜌 2 𝑂 𝑏 𝑂 𝑐 𝑣 2 𝜏 → 0 : Born limit 𝜏 → 1 : unitary limit Scattering rate 𝑏 𝑐 = 𝑜 imp 𝜌𝑂 𝑐 𝑏 𝑣 2 1 − 𝜏 Γ Averaged coupling constant 𝜇 𝐺𝑇 = 𝑂 𝑏 𝜇 𝑏𝑏 + 𝜇 𝑏𝑐 + 𝑂 𝑐 𝑂 𝜇 𝑐𝑏 + 𝜇 𝑐𝑐 𝑂 D.V. Efremov, MMK, O.V. Dolgov, A.A. Golubov, and P.J. Hirschfeld, PRB 84, 180512(R) (2011)
Experiment: disorder Irradiation studies Ba 0.5 K 0.5 Fe 2-2x M 2x As 2 J. Li et al., PRB 85, 214509 (2012) R. Prozorov et al., arXiv:1405.3255v1
Effect of impurity scattering: Born limit 𝑜 𝜚 1 1 = 2𝑈 𝑑 𝜇𝜌𝑂 0 Single-band case: Δ 𝜕 𝑜 𝑈 0<𝜕 𝑜 ≤𝜕 𝐸 𝑑 Nonmagnetic (magnetic) impurities: 𝑜 = 𝜕 𝑜 + Γ 𝑏 𝜕 𝑜 𝑜 𝜚 1 = 1 𝜕 𝑑 = 1.13𝜕 𝐸 𝑓 −1 𝜇𝑂 0 𝑈 2 + 𝜚 2 𝑜 2 Δ 𝜕 𝑜 𝜕 𝑜 𝜕 𝑜 𝑈 𝑑 Anderson’s theorem 𝑜 𝑜 = Δ + Γ 𝑏 𝜚 𝜚 impurities cancel out! − 𝑜 2 + 𝜚 2 𝜚 1 1 𝑜 2 𝜕 𝑜 = Δ 𝜕 𝑜 𝜕 𝑜 + Γ 𝑏 𝑈 𝑑 impurity scattering rate Γ 𝑏 = 𝜌𝑂 0 𝑜 imp 𝑣 2 ln 𝑈 𝑑0 = Ψ 1 2 + Γ 𝑏 − Ψ 1 𝑈 𝑑 is suppressed compared to the clean case ( 𝑈 𝑑0 )! 2 𝑈 2𝜌𝑈 𝑑 𝑑 Magnetic interband-only impurities in the 2-band case: 𝛽𝑜 𝜚 1 = 1 if Δ 𝑏 = −Δ 𝑐 then 𝑈 𝑑 is not suppressed ( 𝑡 ± ) Δ 𝛽 𝜕 𝛽𝑜 𝜕 𝑜 𝑈 𝑑 A.A. Golubov and I.I. Mazin, PRB 55, 15146 (1997), Physica C 243, 153 (1995)
T-matrix approximation for the impurity self-energy imp 𝜕 𝑜 , 𝜚 imp 𝜕 𝑜 𝑏𝑜 = Σ 2𝑏 𝜕 𝑜 + Σ 2𝑏 i𝜕 𝑏𝑜 = i𝜕 𝑜 − Σ 0𝑏 𝜕 𝑜 − Σ 0𝑏 imp 𝜕 𝑜 = 𝑜 imp 𝐕 imp 𝜕 𝑜 + 𝐕 𝐡 𝚻 𝜕 𝑜 𝚻 imp imp imp 𝐽 𝐾 𝐽 Σ 𝑏𝑏 Σ 𝑐𝑏 Σ 𝑏𝑏 imp imp imp 𝐾 𝐽 𝐾 Σ 𝑐𝑏 Σ 𝑐𝑏 Σ 𝑏𝑏 𝑜 imp is the impurity concentration 𝐽𝑇 𝐾𝑇 = Impurity potential 𝐕 𝐽 and 𝐾 are the impurity potentials 𝐾𝑇 𝐽𝑇 Effective impurity scattering strength Generalized cross-section parameter 2𝜌𝐾 2 𝑡 2 𝑜 imp 𝑂 𝑐,𝑏 , (helps to control the approximation) Born 2𝑜 imp 𝜏 𝜌 2 𝐾 2 𝑡 2 𝑂 𝑏 𝑂 𝑐 → 0, Born 2𝑜 imp Γ 𝑏,𝑐 = → unitary 𝜏 = 𝜌𝑂 𝑏,𝑐 unitary , 1, 1 + 𝜌 2 𝐾 2 𝑡 2 𝑂 𝑏 𝑂 𝑐 𝜌𝑂 𝑏,𝑐
Interband magnetic impurities: results for the 𝑡 ± and 𝑡 ++ systems Interband-only impurities unitary unitary do not destroy 𝑡 ± superconductivity Born This confirms qualitative arguments that Born 𝑡 ± state with magnetic disorder behave like the 𝑡 ++ state with non-magnetic impurities [Golubov, Mazin (1995,1997)] and agrees with the Born limit results [Li, Wang, EPL 88, 17009, (2009)]. 𝒕 ++ → 𝒕 ± transition! 𝛽𝑜 /𝑎 𝛽𝑜 Δ 𝛽𝑜 = 𝜚 Then 𝑈 𝑑 saturates since the 𝑎 𝛽𝑜 = 𝜕 𝛽𝑜 /𝜕 𝑜 interband-only impurities do not destroy 𝑡 ± state. It is the only way for the 𝑡 ++ state to be robust against the magnetic disorder. Smaller gap changes sign for Γ > 40 cm −1 !
Finite intraband magnetic disorder: 𝑡 ± and 𝑡 ++ systems Interband-only unitary impurities do not destroy 𝑡 ± superconductivity, but intraband do ! Born Finite intraband disorder finally suppress 𝑑 to zero. 𝑈 𝒕 ++ → 𝒕 ± transition can’t save 𝑡 ++ state from being destroyed. The only exception here is the unitary limit ( 𝜏 = 1 ). At 𝑈 → 𝑈 𝑑 : Γ 𝑏 𝜕 𝑏𝑜 = 𝜕 𝑜 + iΣ 0𝑏 𝜕 𝑜 + 2 sgn 𝜕 𝑜 𝑏𝑜 Γ 𝑏 𝜚 𝑏𝑜 = Σ 2𝑏 𝜕 𝑜 + 𝑏𝑜 𝜚 2 𝜕
DOS and penetration depth in 𝑡 ± and 𝑡 ++ systems = 𝐾/2 𝐾 𝑊 𝐾/2 𝐾 𝜏 → 0 : Born limit 𝒕 ++ → 𝒕 ± transition 𝜏 → 1 : unitary limit
Conclusions The 𝑼 𝒅 suppression is much slower than suggested in AG theory • There are few exceptional cases with the saturation of 𝑼 𝒅 for the finite • amount of magnetic impurities: • (1) s ± superconductor with the purely interband impurity scattering potential. • (2) s ++ state with the interband-only scattering due to the s ++ → s ± transition. Since this transition goes through the gapless regime, there should be clear signatures in the thermodynamics of the system. Therefore, it may manifest itself in optical and tunneling experiments, as well as in a photoemission and thermal conductivity on Fe-based superconductors and other multiband systems. • (3) the unitary scattering limit MMK, D.V. Efremov, A.A. Golubov, O.V. Dolgov, PRB 90, 134517 (2014)
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