Violation of Anderson‘s 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:

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

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 ← ρ ∝ T Kasahara et al. arXiv (’09) ρ ∝ T 2 → H. Luo et al. Supercond. Sci. Technol. (’08) BaFe 2 (As 1-x P x ) 2

Nonmagnetic impurity effect k k’ -k’ -k inter-FS scattering of Cooper pair (±k ⇔ ±k’) Naïve expectation: S±-state is weak against impurities due to inter-FS scattering between hole (Δ>0) and electron (Δ<0) pockets. Inter-FS T-matrix AG theory for S±-wave model: Tc vanishes when  inter ~0.6T c0 depairing for S±-wave: violation of Anderson’s theorem  /2 Chubukov et al., PRB 78, (2008). Parker et al., PRB 78, (2008).

Coherence length  v F /  ・ 122-system:  ~10a Fe-Fe (~27 Å ) ・ YBCO (optimum):  ~4a Cu-Cu (~16 Å ) ・ NCCO (optimum):  ~20a Cu-Cu (~80 Å ) In general, 2  inter ~  (=QP damping) in the absence of Anderson’s theorem (|T ii |~|T i≠j |). ⇒ Tc vanishes when l mfp ~2.5  [l mfp =v F /2  ]

Fe-site substitution ● The impurity potential is diagonal w.r.t d-orbital: I ・  d,d’ (d,d’=xz,yz,x 2 -y 2, …) →band diagonal basis: :(I,I’)-model If we consider only the inter-FS scattering I’, ⇒ S±-state is robust against impurities if I’/I≠1. X + X XX + … odd-order terms The above approximation (I i,j (k,k’)→I,I’) is dangerous in FeAs! Kulic (’99), Ohashi(’02), Senga and Kontani (’08) approximately, Onari and Kontani, arXiv (’09) Inter-band T-matrix:

Fe-site substitution （ Co,Ni,Zn,Ru,Ir, … ） : robustness of the superconducting state L. Fang et al. arXiv: d 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?)

F. Han et al., arXiv: 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)

First principle study for the impurity potential ・ Impurity radius ~ 1 Å≪ a Fe-Fe ⇒ local impurity ・ I ～ +1.5eV (IN(0)>1) 1Å1Å A.F. Kemper et al., arXiv: Fe-site substitution by Co Co site =2.7 Å Site-selective NMR at As site F.L. Ning et al., arXiv:

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

Study of impurity effect based on the five-orbital model Kuroki et al., PRL (’08) (1) BCS Nambu Hamiltonian in the d-orbital basis (10×10): (2) Green function (10×10): normal Green fn.anomalous Green fn. in band-diagonal basis

T-matrix approximation in the five-orbital model (4) self-energy (10×10): (3) T-matrix in the d-orbital basis (10×10): (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.

If we replace with, Anderson’s 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/% Anderson’s theorem is violated! ・ Impurity potential in the band basis: |

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) ∞  imp (μΩcm) Experimentally,  imp >30 μΩcm (single←poly) for 1% Co impurity. M. Sato et al., arXiv:

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

・ in the S± wave: (violation of Anderson’s 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.

● 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

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

Summary 1 ・ S± state is fragile against impurities: (violation of Anderson’s 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: