I. Review of Fe-based Superconductivity II. Disorder effects in unconventional SC

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1 I. Review of Fe-based Superconductivity II. Disorder effects in unconventional SC P. Hirschfeld, U. Florida Maglab Theory Winter School January 2013 Balatsky, Vekhter and Zhu, Rev Mod Phys 78, 373, (2006) Alloul, Bobroff, Gabay, PH, Rev. Mod. Phys. 81, 45 (2009)

2 Anderson s theorem P. W. Anderson, J.Phys. Chem. Solids 11, 26 (1959) In the presence of dirt one can still pair time-reversed members of Kramer s doublet: thermodynamics (T c, gap, sp. ht., ) are not affected by nonmagnetic impurities

3 Abrikosov-Gor kov theory Many body formulation of disorder problem in superconductor assuming weak scattering agrees with Anderson conclusions

4 Abrikosov-Gor kov theory cont d Skalski et al PR 136, A Pairbreaking in s-wave SC by magnetic impurities Gapless SC

5 Balian-Werthamer: p-wave superconductivity Nonmagnetic impurities are pairbreaking in unconventional superconductors

6 Strong magnetic impurity creates bound state in s-wave SC Yu Lu, Acta Physica Sinica 21, 75 (1965) see also H. Shiba, Prog. Theor. Phys. 40, 435 (1968). A. I., Rusinov, 1969, Zh. Eksp. i Teor. Fiz. 56, 2047, [Sov. Phys. JETP 29, 1101 (1969)].

7 T-matrix for single nonmagnetic impurity U U U i j = G G G UG G UG UG T = G + G TG = + + +, where = U + UG U + UG UG U +... = U + UG T Onsite potential Ui () = uδ ( i i) T ( ω) = 0 0 u G k ( k, ω)

8 Magnetic impurity bound state in s-wave SC G 0 = ( ωτ ξ τ iσ τ ) 0 k τ 3 1 τ 3 U = uss α = uss σ + σ 2σσ T = U + UG T = u [ ] G 0 + us τ0 + G 1 us s (1 ) (1 ) τ + ω 1 2us + u 2 2 ω s 1 subgap state Pole ω=ω 0

9 Impurity bound state in s-wave superconductor? G cc cc ωτ + ξ τ + τ 0 0 k 3 1 = = cc cc ω ξk Nambu propagator

10 bound state in s-wave superconductor? Impurity bound state in s-wave superconductor? G cc cc ωτ + ξ τ + τ 0 0 k 3 1 = = cc cc ω ξ k T 0 = U + UG T U = uτδ( i i 0 = u0τ3 + u0τ 3 k G ( k, ω) Σ T )

11 Impurity bound state in s-wave superconductor? G cc cc ωτ + ξ τ + τ 0 0 k 3 1 = = cc cc ω ξk T 0 = U + UG T U = uτδ( i i 0 = uτ + uτ Σ G ( k, ω) T T k 1 α )= Σ 2 G ( ω Tr τ G ( k, ω) G0τ0 G1τ u iω 1 0 = 2 ; α 2 2 = u0 + G1 G0 ω = i α = ω ) k α 0

12 Impurity bound state in s-wave superconductor? T G cc cc ωτ + ξ τ + τ 0 0 k 3 1 = = cc cc ω ξk 0 = U + UG T U = uτδ( i i 0 = uτ + uτ Σ G ( k, ω) T k 1 α )= Σ 2 G ( ω Tr τ G ( k, ω) G0τ0 G1τ1 iω T = ; α = 0 u0 + G1 G ω = u i α = 1 No! no pole (Anderson, AG) 2 2 ω ) k α 0

13 What about in d-wave superconductor? G ωτ + ξ τ + ( φ ) τ = ω ξ φ) k k ( ( φ) = 0 cos 2φ

14 What about in d-wave superconductor? G ωτ + ξ τ + ( φ ) τ = ω ξ φ) k k ( ( φ) = 0 cos 2φ T = 1 G τ Gτ u G0 ( ω )= ; u G G ω ( φ) φ G 1 ( ω )= ω iω 2 2 i ( φ ) ( φ) 2 2 φ

15 Nonmagnetic impurity in d- or s -wave superconductor? G ωτ + ξ τ + ( φ ) τ = ω ξ φ) k k ( ( φ) = 0 cos 2φ T = Possible pole 1 G0τ0 G1τ1 u0 0( 2 ; G ω )= 2 2 u0 + G1 G0 ω ( φ) φ u G 0 G 1 ( ω )= ω iω 2 2 i ( φ ) ( φ) 2 2 φ = 0! for d-wave

16 Bound states of nonmagnetic impurity in d-wave SC 1 ρ(, rω) = Im Grr (,; ω) π δρ imp see also Stamp, 1986 (p-wave)

17 Nonmagnetic impurity bound states in various systems

18 Finite nonmagnetic disorder in unconventional superconductors

19 (Weak nonmagnetic) disorder and unconventional superconductors: destruction of gap nodes Gor kov and Kalugin, Sov. Phys. JETP 41, 253 (1985) Rice and Ueda, Theory of Heavy Fermions and Valence Fluctuations (Springer, 1985) Self-consistent treatment of average G: Σ predictions for residual dos N(0) in p-wave states ``polar state (θ)=cos θ ``axial state (θ)=sin θ N(0)>0 for infinitesimal disorder N(0)>0 for critical disorder strength triplet classes with point nodes (with moment) are `topologically stable

20 PH et al Sol St. Comm 59, 111 (1986) Schmitt-Rink et al, PRL 57, 2575 (1986)

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22 :

23 (cuprates, heavy fermions) (Zn, Li, vacancy ) Universal

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25 Pan et al, Nature 403, 746 (2000). T = 4.2 K 200 pa, -200 mv ~20 Zn atoms Å Bi 2 Sr 2 Ca(Cu 1-x Zn x ) 2 O 8+δ : x 0.3% LDOS map at 1.5mV! Å

26 Zn On-site LDOS spectrum: Ω 0 =-1.5 mev 2.5 Differential Conductance (ns) Sample Bias (mv) Pan et al, Nature 403, 746 (2000).

27 F i, j θ j k-space r-space F i, j Å θ j Data contrast with naïve expectation: Y 2 should be a four-fold symmetric star oriented with gap-nodes, maximum amplitude on nearest neighbor sites!

28 Spatial structure of these Ψ 2 not well understood. Zn Ni Cu:Vac.? -1.2 mv +9 mv 0 mv 0 Å 30 Å 0 Å 32 Å 0 Å 32 Å

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30 Theories of impurity resonance spatial pattern Chemistry : M.E. Flatté et al. 2001, 03. Assume generalized extended impurity potential. Filter : C.S. Ting et al. 2001, Martin & Balatsky STM probes LDOS of neighboring Cu s due to k-dependent tunneling matrix elements. Correlations : Polkovnikov et al 2001, account for Kondo screening of correlation-induced local moment

31 Back to FeSC: intriguing defect states whose structure may reveal SC gap those shown believed to be Fe vacancies (J.E. Hoffman) 1111 (LaFeAsO) 111 (LiFeAs) 11 (FeSe) 10nm Zhou, PRL 106, (2011) Hanaguri, unpublished 10nm Song, Science 332, 1410 (2011)

32 Sometimes no impurity bound states are seen Na(Fe 1-x Co x )As Yang et al, PRB 86, (2012) but it is not surprising! 5-orbital BdG: Kariyado and Ogata, JPSJ 79, (2010). bound states are hard to tune to low E PH et al, ROPP 74, (2011) Beaird et al PRB 86, (2012) U 11 N 0 (intraband) Ω 0 S+/- state U 12 N 0 (interband)

33 How to simplify many-parameter problem II: use ab initio methods to determine intra/interband character of scattering? Ratio V inter /V intra important Impurity diagonal in orbital space has generically large interband component (Kontani 2009) Answer question with ab initio calculations for specific defects Kemper et al 2009 for Co band space: U U Kemper et al 2009, Nakamura et al 2010 Disagreement between Kemper, Nakamura, Elfimov on Co potential?

34 s ++ or s +-? Few phase-sensitive expts. Chen et al, Nature 2010 Christianson et al Nature 2008 Hanaguri et al Science 2010 NdFeAsO 0.88 F 0.12 Half-integer fluxes detected (in a small fraction of loops) Ba 0.6 K 0.4 Fe 2 As 2 Enhanced susceptibility at Q below Tc sign change of order parameter Fe(Se,Te) Field dependence of quasiparticle interference peaks depends on order parameter sign Various critiques of all experiments, alternate scenarios: where is the?

35 Hiroshi Kontani, M2S 2012

36 Hiroshi Kontani, M2S 2012

37 Inter- and intraband impurity scattering in 2-band s +/- system Inter- k -k k k mixes + and gaps, breaks pairs Intra- k -k k k k k k -k no mixing of +/- no pairbreaking

38 Scenario 1: isotropic s +/- state + interband impurity scattering low-e power laws ~ T if N( ω = 0) = const N(ω) ω Parker et al PRB 2008 Chubukov et.al., PRB 2008 Vorontsov et al PRB 2009 s +/- state has full gap but interband scattering is pairbreaking due to bound state

39 Scenario 2: anisotropic states with intraband scattering recall Fletcher et al 2008 LaFePO T c =6K λ~t nodes! Mishra et al PRB 2009 small-q scattering clean intraband scattering averages gap anisotropy, lifts nodes! dirty

40 Simplest problem: T c suppression in s +/- state naïve expectations: interband scattering will suppress T c faster T c suppression will depend on interband/intraband scattering potential ratio u/v T c suppression will depend on ratio/signs of interband/intraband pairing λ inter /λ intra as well

41 2-band disorder problem self-consistent t-matrix approx. interband Preosti, Muzikar PRB 54, ; Golubov, Mazin, Phys. Rev. B 55,

42 Electron irradiation at LSI (Irradiated Solids Lab)--Paris Pelletron Facility At LSI vacancy interstitial (Frenkel) pairs different sublattices are affected, depending on beam energy initial paper: arxiv: with 2.5MeV electrons: dominant Fe vacancies Shibauchi Matsuda Rullier-Albenque Prozorov also: C. van der Beek, M. Konczykowski Thanks: C. van der Beek

43 e- irradiation experiments Ba(Fe0.74Ru0.26)2As2

44 theory Wang et al 2012 (unpublished) (φ) α β φ u = inter band impurity potential v =intra band impurity potential (φ) φ Critical ρ 0 s range from 20µΩ cm to mω-cm!

45 e- irradiation of BaFe 2 (As,P) 2 Nonmonotonic change of low T dependence: T exp(- /T) T 2

46 DOS, λ, T 1-1 with increasing disorder: mixed inter and intraband scattering disorder N(ω) (φ) φ N(ω) (φ) (φ) φ φ N(ω) N(ω) (φ) φ ω ω ω e - /T λ ~ T T 2 T 2 T -1 1 ~ T 3 T e - /T T ω

47 (φ) φ S +/- Theory of nonmonotonic λ(t)-variations Wang et al 2012 (unpublished) (φ) S ++ φ pairbreaking at nodes node lifting s +- bound state formation α=u/v Only s+/- can explain data!

48 Comparison: expt vs. theory

49 Conclusions Unconventional superconductors are generically sensitive to nonmagnetic disorder impurity bound states may be good probes of superconducting gap structure; mysteries remain e- irradiation experiments: T c suppression, penetration depth experiments strong evidence for sign-changing in FeSC To use disorder analysis to determine order parameter structure, need to reduce # parameters ab initio methods?