Back to the Iron age the physics of Fe-pnictides

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1 Back to the Iron age the physics of Fe-pnictides Andrey Chubukov University of Wisconsin Texas A & M, Dec. 4, 2009

2 Fe-Pnictides: Binary componds of pnictogens A pnictogen an element from the nitrogen group N,P, As,Sb,Bi RFeAsO (1111) R = La, Nd, Sm, Pr, Gd AFe2As2 (122) A = Ba, Sr, Ca LiFeAs (111) IRON AGE ( B.C.E.) LaOFeP FeTe

3 Fe-Superconductors, Tc Compound (powder & single crystals) Tc Reference LaOFeP ~5 K Y. Kamihara et al., J. Am. Chem. Soc.128, (2006) LaNiOP ~3 K T. Watanabe et al., Inorg. Chem. 46, 7719 (2007) La[O1-xF-x]FeAs La[O1-xCa2+x]FeAs 26 K (x= ) 0K Y. Kamihara et al., J. Am. Chem. Soc.130, 3296 (2008) La[O1-xFx]NiAs 3.8 K (x=0.1)2.75 K (x=0) Z. Li et al., arxiv: (La1 xsrx)onias 3.7 K (x= ) 2.75 K (x=0) L. Fang et al., arxiv: (La1 xsrx)ofeas 25 K (x=0.13) H.-H. Wen et al., EPL 82, (2008) Ce[O1 xfx]feas 41 K (x=0.2) G.F. Chen et al., PRL 100, (2008) Pr[O1-xFx]FeAs Nd[O1-xFx]FeAs 52 K (x=0.11) Z.-A. Ren et al., arxiv: ; Z.A. Ren et al., EPL, 82 (2008) Gd[O1 xfx]feas 36 K (x=0.17) P. Cheng et al., Science China 51(6), (2008). Sm[O1 xfx]feas 55 K (x= ) Z.-A. Ren et al., Chin. Phys. Lett. 25, (2008); R.H. Liu et al., arxiv:

4 Crystal structure Folded BZ Unfolded BZ LaFeAsO 2D Fe-As layers with As above and below a square lattice formed by Fe

5 Are pnictides similar to cuprates? Pnictides Cuprates Parent compounds are antiferromagnets Superconductivity emerges upon doping

6 TUG-OF-WAR (the rope is borrowed from cuprates) Similar Abrahams, Bernevig, Haule, Kivelson, Kotliar, Phillips, Sachdev, Si, Sushkov, Xu. Different Carbotte, Gorkov, Hirschfeld, D-H Lee, Mazin, Scalapino, Schmalian, Tesanovic, Vishwanath.

7 Cuprate high Tc superconductors metal Mott insulator Heisenberg antiferromagnet metal

8 Fe-Pnictides metal metal

9 I. Metallic behavior in the magnetic phase TN 0

10 II. Band theory calculations agree with experiments Lebegue, Mazin et al, Singh & Du, Cvetkovic & Tesanovic Electron Fermi surface Hole Fermi surface 2 hole pockets around (0,0) 2 electron pockets around (π,π) (folded BZ), or (0,π) and (π,0 ) (unfolded BZ)

11 ARPES NdFeAs(O1-xFx) (x=0.1) A. Kaminski et al. dhva Ba06K04Fe2As2 H. Ding et al. D. Evtushinsky et al Hole pockets near (0,0) Electron pockets near (π,π) LaFeOP A. Coldea et al,

12 Itinerant approach Magnetism

13 The system remains a metal the magnetic phase TN 0

14 Magnetic order (π,0) or (0,π) in the unfolded BZ (π,π) in the folded BZ

15 Itinerant description: magnetism comes from nesting Dong et al, Korshunov & Eremin, Raghu et al., K. Kuroki et al,

16 Nesting is a boost for an SDW antiferromagnetism = χ 0 (Q) = T ε ke dω dε k F = log ω 2 + ε k2 T ε k+q χ 0 (Q) χ (Q) = 1 - U χ 0 (Q) For a perfect nesting, AFM instability occurs already at small U M. Rice (for Cr), Z.Tesanovic,. V. Cvetkovic and (π,π) in the folded BZ 2kF Eremin & Korshunov

17 Questions 1. The actual order is (π,0) (π,π) folded BZ Q1 = (π,0) Q2 = (0,π) i Q r i Q r 1 S = S1 e + S2 e 2 2. Why the system remains a metal? SDW SDW gaps

18 1. Selection of a magnetic order Introduce two SDW order parameters V ( 2 2 E gr = F W1 + W2 ( ) W1 with Q1 = (0, π ), W2 with Q 2 = (π,0) O(6) symmetry ) E gr = F W1 + W2 + a V (W1 ) (W2 ), a > 0 Either W1 =0, (0,π) state Or W2 =0, (π,0 ) state

19 2. Metallicity doubly degenerate Q1 Q2 a metal Zhou et al Borisenko et al

20 Itinerant approach Superconductivity

21 Electron-phonon interaction is too weak Boeri, Dolgov, & Golubov, Singh & Du λ=0.44 for Al Too small to account for Tc =50K

22 Pairing due to el-el interaction How about using the analogy with the cuprates and assume that the pairing is mediated by spin fluctuations peaked at (π,π) Mazin et al, Kuroki et al. Cuprates + Pnictides I. Mazin et al., PRL 101, (2008) (θ ) = 0 (cos k x - cos k y ) (θ ) = 0 (cos k x + cos k y ) sign-changing extended s-wave gap

23 Experiments

24 Some experiments are consistent with +no-nodal s gap

25 1. Photoemission in 1111 and 122 FeAs Ba1-xKxFe2As2 NdFeAsO1-xFx T. Kondo et al., arxiv: D. Evtushinsky et al Almost angle-independent

26 2. Neutron scattering resonance peak below 2D T < Tc (π,π) T > Tc Christianson etal. Ba0.6K0.4Fe2As2 Theory : need k +π = - k The plus-minus gap is the best candidate Eremin & Korshunov Scalapino & Maier

27 3. Penetration depth behavior in 1111 and 122 FeAs SmOFeAs Ba1-xKxFe2As2 Ba0.46K0.56Fe2As2 Carrington et al Exponential behavior at low T (or, at least, a very flat behavior) Y. Matsuda

28 Other experiments, howecver, indicate that the gap may have nodes

29 1. NMR and Knight shift in 1111 FeAs Knight shift NMR relaxation rate Matano et al Non-exponential behavior!

30 2. The behavior of BaFe2(As1-xPx)2, Tc =30K Y. Matsuda et al BaFe(AsP) (BaK)FeAs Nodes in BaFe2(As1-xPx)2,

31 Back to simple reasoning There is a problem: how to get rid of an intra-band Hubbard repulsion? Cuprates (θ ) d θ = 0 FS Pnictides (θ ) d θ 0 FS Intra-band repulsion does not Hubbard repulsion cancels out, only d-wave, cancel and has to be overtaken (π,π) interaction matters by a (π,π) interaction

32 f-fermions u4 u3 u5 Theory The two-band nested Fermi liquid with intra-band and inter-band interactions c-fermions = density of states in 2D Intra-band repulsion u4 =u5 Pair hopping (π,π) interaction Inter-band forward and back-scattering

33 Let s see how pair hoping and intra-band repulsion compete 1. Spin density wave χ SDW = ( χ SDW ) 0 1 (Γ SDW ) 0 Π sdw Π sdw log EF T nesting The system surely favors an SDW instability Γ0SDW = u 3 + u1 > 0, 2. S+ superconductivity (Γ ) SC s+ 0 χ SC s+ ( χ ssc+ ) 0 = 1 (ΓsSC + ) 0 Π sc Π sc log EF T If intra-band repulsion (u4) is = u 3 - u 4, stronger than the pair hopping (u3), the pairing interaction is repulsive Orbital model -> band model: u4 > u3 SDW magnetism, but no superconductivity

34 Two ways to go beyond this level of consideration and obtain superconductivity Maxim Vavilov Anton Vorontsov Ilya Eremin Dmitry Efremov, Maxim Korshunov

35 I. Explore nesting AND the smallness of the pockets The terms in the Hamiltonian are bare interactions, at energies comparable to a fermionic bandwidth We, however, need interactions at energies smaller than the Fermi energy [we have log EF/T] 0 EF ~ 0.1 ev W ~2 ev E Couplings flow due to renormalizations by particle-particle and particle-hole bubbles

36 We know this story for conventional (phonon) superconductors ωd EF ~ W 0 E Coulomb repulsion is renormalized down by the renormalization in the particle-particle channel (McMillan-Tolmachev renormalization) If only Cooper channel is involved, this cannot change a repulsion into an attraction u 4 u3 = (u 4 u 3 ) (u 4 u 3 ) 0 log W/E In our case, there are renormalizations in both particle-particle AND particle hole channel. This implies that we need to construct parquet RG to analyze the system flow between W and EF (H. Shultz, Dzyaloshinskii & Yakovenko)

37 Parquet RG The pair hopping term is pushed up by the density-density interaction u1 responsible for a SDW order

38 One-loop parquet RG The fixed point: the pair hopping term u is the largest 3 u3 1/ 3 u1 = - u 4 = - u 5 =, u2 u3 5 u0l

39 One-loop RG Flow SDW with real order parameter CDW with imaginary order parameter Extended swave In the process of RG flow, the interaction in the extended s-wave channel becomes attractive Numerical RG : F. Wang, H. Zhai, Y. Ran, A. Vishwanath, and D.- H. Lee C. Platt, C. Honerkamp, and W. Hanke

40 Perfect nesting SDW wins Non-perfect nesting SDW vertex remains the strongest, but the SDW instability is cut, and a node-less s+ SC wins

41 However, Parquet RG stops at E ~ EF u0lmax = u0 log W/EF A sign-changing, nodeless s+ gap does not emerge No s+ pairing? + u0lmax 0 (θ ) = 0 (cos k x + cos k y )

42 II. Let s include momentum-dependent part of the pair hopping The idea: if the gap averages to zero along either hole or electron FSs, or both, the effect of intra-pocket repulsion will be eliminated, at least partly u 3 (p) = u ~ u 3 cos py ~ px cos +~ u 3 (cos p x + cos p y ) The expansion in the size of a Femi pocket qy qx (q) = 0 (cos q x + cos q y ) + 1 cos cos + 2 (cos q x cos q y ) a plus-minus gap an s-wave gap with nodes on electron FSs a d-wave gap with nodes on all FSs

43 py px ~ u 3 (p) = u u 3 cos cos 2 2 qy qx (q) = 0 (cos q x + cos q y ) + 1 cos cos 2 2 Solve three coupled BCS equations for the gaps: When is zero, the solution L >0 exists only for u3>u4 When is non-zero, the solution exists for arbitrary u3/u4 and has nodes for u3>u4,

44 Gap symmetry does not change! s+ gap with the nodes on electron FS s+ gap with no nodes 1 Less SDW fluctuations Underdoped 1111, 122 FeAs LaFeOP, BaFe2(As1-xPx)2 Overdoped 1111, 122 FeAs

45 Conclusions: Fe-pnictides are itinerant systems, no evidence for Mott physics Magnetism is of SDW type, the system remains a metal Superconductivity is the result of the interplay between intra-pocket repulsion and the pair hopping. If the tendency towards SDW is strong, pair hopping increases in the RG flow, and the system develops an s+- gap without nodes, once SDW order is eliminated by doping. If the tendency towards SDW is weaker, intra-pocket repulsion remains the strongest. The system still becomes an s+- supercnductor, but the gap has nodes along the two electron Fermi surfaces.

46 THANK YOU