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Violation of Andersons Theorem for the s-wave Superconducting State in the Five-Orbital Model for FeAs S. Onari (Nagoya Univ.) H. Kontani (Nagoya Univ.) S. Onari and H. Kontani, arXiv:0906.2269

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Content of the presents talk recent experimental results (Fe-site substitution, coherence length, NMR, ) theoretical study of impurity effect (a) constant (I,I)-model in the band basis [frequently-used, but oversimplified] (b) realistic five-orbital model Kuroki et al., PRL (08) large interband scattering due to multiorbital strong depairing for S state Tc, superconducting DOS, residual resistivity, Message Impurity effect offers us significant information in studying superconductivity. Contents

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AF fluctuations S-wave state Suhl-Kondo mechanism RPA, FLEX, 3 rd U, RG, spin fluctuation mechanism for S wave state Kuroki, Mazin, D.H. Lee, Nomura, evidence for AF fluctuations T Kasahara et al. arXiv (09) T 2 H. Luo et al. Supercond. Sci. Technol. (08) BaFe 2 (As 1-x P x ) 2

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Nonmagnetic impurity effect k k -k -k inter-FS scattering of Cooper pair (k k) Nave expectation: S-state is weak against impurities due to inter-FS scattering between hole (>0) and electron (

Fe-site substitution Co,Ni,Zn,Ru,Ir, : robustness of the superconducting state L. Fang et al. arXiv:0903.2418 3d FeCoNi 4d RuRhPd 5d (Os)Ir(Pt) Ba(Fe 1-x M x ) 2 As 2 M=Co (Rh,Ir) T c max ~30K This result will be difficult to understand if T c >100 K for n imp =0.1 like in high-Tc cuprates. (d-wave superconductor) reduction in Tc x c =0.17 carrier doping impurity potential (Born? Unitary?)

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F. Han et al., arXiv:0906.0403 Sr(Fe 1-x M x ) 2 As 2 ; M=Rh, Ir n imp =30% Bulk SC Tc is finite even for n imp ~40%! 3d FeCoNi 4d RuRhPd 5d (Os)Ir(Pt)

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First principle study for the impurity potential Impurity radius ~ 1 a Fe-Fe local impurity I +1.5eV (IN(0)>1) 11 A.F. Kemper et al., arXiv:0904.1257 Fe-site substitution by Co Co site =2.7 Site-selective NMR at As site F.L. Ning et al., arXiv:0907.3875

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Fe 1+ Te 1-x Se x T.J. Liu et al., arXiv:0904.0824 =0.03, x=0.4 =0.13, x=0.4 (bilk SC) >400cm just above Tc (single crystal) l mfp ~ a Fe-Fe superconductivity (Tc~10K) in the Ioffe-Regel limit! 1.0 0 Band calculation Lee and Pickett, arXiv:0908.2698 no Fe 3d hole-pockets no nesting: new class FeAs? Sr 2 VO 3 FeAs (Tc=37K) Fe 3d orbital

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Study of impurity effect based on the five-orbital model Kuroki et al., PRL (08) (1) BCS Nambu Hamiltonian in the d-orbital basis (1010): (2) Green function (1010): normal Green fn.anomalous Green fn. in band-diagonal basis

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T-matrix approximation in the five-orbital model (4) self-energy (1010): (3) T-matrix in the d-orbital basis (1010): (5) gap eq.: In the fully self-consistent approximation, we solve eqs. (1)-(5) self-consistently. In calculating the DOS, we solve eqs. (1)-(4) putting in as constant for simplisity.

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If we replace with, Andersons theorem holds for I= like in (I,I)-model. Impurity-induced DOS in the S wave In five-orbital model, S DOS is broken only by 1% unitary (I=) impurities. reduction in Tc is >10K/% Andersons theorem is violated! Impurity potential in the band basis: |

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Small impurity effect in the S++ wave The gap structure in the S++ state is robust against impurities. reduction in Tc is small (a check of numerical calculation) Residual resistivity Damping rate for I=+1eV is the largest due to strong p-h asymmetry. residual resistivity for n imp =1% I(eV)-4.5+1+4.5 imp (cm) 73221410 Experimentally, imp >30 cm (singlepoly) for 1% Co impurity. M. Sato et al., arXiv:0907.3007

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Impurity effect on Tc In the d-orbital representation, Tc is obtained by solving the linearized gap equation.

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in the S wave: (violation of Andersons theorem) is renormalized to [z=m/m * ] Numerical result g 2,3 If z=0.5, Tc vanishes when n imp ~0.01 for I=1eV.

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large residual resistivity (finite T) in high-Tc cuprates Fukuzumi et al., PRL (96) YBCO Tc =10~20K/% in high-Tc cuprates (Zn-doping) Tallon et al., PRL (97) underdope

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enhanced residual resistivity near AF-QCP Kontani and Ohno: PRB (06) FLEX+single-impurity potential: by unitary local impurity (U=0). underdopeoverdope

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Summary 1 S state is fragile against impurities: (violation of Andersons theorem) quantitative study of impurity effect based on the five-orbital model. S state may be more stable when (i) |I| 1eV (ii) potential radius a Fe-Fe (iii) very strong coupling ( 10a Fe-Fe ) long-range impurity potentials What is the pairing mechanism if S++ state occurs? arXiv:0906.2269