Interplay between magnetism and superconductivity in Fe-pnictides

1. Interplay between magnetism and superconductivity in Fe-pnictides Andrey Chubukov University of Wisconsin Institute for Physics Problems, Moscow, June 30, 2010

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 Tc,max =57K (SmFeAsO) AFe2As2 (122) A = Ba, Sr, Ca LiFeAs (111) LaOFeP Fe(SeTe) IRON AGE (1200 - 550 B.C.E.)

3. Fe-pnictides: May 2006 2006 Hideo Hosono, TITech 2008

4. Tc (K) Gd1-xThxFeAsO SmFeAsO1-x SmFeAsO1-xFx PrFeAsO1-xFx Tb1-xThxFeAsO GdFeAsO1-x NdFeAsO1-xFx TbFeAsO1-xFx DyFeAsO1-xFx SmFeAsO1-xFx Sr1-xKxFe2As2 CeFeAsO1-xFx Ba1-xKxFe2As2 GdFeAsO1-xFx Eu1-xKxFe2As2 LaFeAsO1-xFx BaCoxFe2-xAs2 Ca1-xNaxFe2As2 La1-xSrxFeAsO BaNixFe2-xAs2 Eu1-xLaxFe2As2 SrCoxFe2-xAs2 Li1-xFeAs FeSe0.5Te0.5 a-FeSe1-x LaO1-xFxFeP a-FeSe LaO1-xNiBi BaNi2P2 LaOFeP LaONiP SrNi2As2 2008 courtesy of J. Hoffman

5. Phase diagram: magnetism and superconductivity Luetkens et al Fernandes et al BaFe2(As1-xPx)2 Matsuda et al

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

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

8. Are pnictides similar to cuprates? Pnictides Cuprates metal Mott insulator/ Heisenberg AFM

9. Metallic behavior of parent compounds TN 0

10. Resistivity in the cuprates parent compounds (magnetic)

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

12. ARPES dHVa LaFeOP NdFeAs(O1-xFx) (x=0.1) Ba06K04Fe2As2 A. Coldea et al, A. Kaminski et al. H. Ding et al. LiFeAs A. Kordyuk et al Hole pockets near (0,0) Electron pockets near (p,p)

13. Fe-pnictides are doped metals High Tc cuprates are doped Mott insulators

14. A simple way to understand the difference between cuprates and pnictides Tesanovic, Physics 2, 60 (2009) 9 one hole in a filled d-shell (1 “free” fermion per cite: half-filling) Cuprates: U Only when doped with holes (or electrons) do cuprates turn into superconductors

15. Pnictides: 4 holes per cite – multiband structure. chemical potential lies in the gap LaOFeAs

16. Itinerant approach Interacting fermions with hole and electron Fermi surfaces, no localization of electronic states What are generic, model-independent features of Fe-pnictides?

17. Magnetic and superconducting properties are both interesting I will skip magnetism and focus only on superconductivity

18. Superconductivity

19. Electron-phonon interaction is probably too weak Boeri, Dolgov, & Golubov, Singh & Du =0.44 for Al Too small to account for Tc ~ 50K

20. I. Mazin et al., PRL 101, 057003 (2008) 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 (p,p) Mazin et al, Kuroki et al…. Cuprates Pnictides 0 sign-changing s-wave gap (s+-)

21. Some experiments are consistent with the sign-changing, no-nodal s+- gap

22. 1a. Photoemission in 1111 and 122 FeAs Ba1-xKxFe2As2 D. Evtushinsky et al NdFeAsO1-xFx T. Kondo et al., arXiv:0807.0815 Almost angle-independent gap (consistent with no-nodal s-wave)

23. 1b. Penetration depth behavior in 1111 and 122 FeAs SmOFeAs Ba1-xKxFe2As2 Ba0.46K0.56Fe2As2 Carrington et al Y. Matsuda “Exponential” behavior at low T (or, at least, a very flat behavior)

24. 1c. Neutron scattering – resonance peak below 2D s+- gap D. Inosov et al. Eremin & Korshunov Scalapino & Maier The “plus-minus” gap is the best candidate

25. Other experiments, however, indicate that the gap may have nodes

26. 2a. The behavior of LaOFeP, Tc =5K Penetration depth Thermal conductivity Residual term in k/T, H1/2 field dependence Linear in T dependence at small T Matsuda et al Consistent with line nodes Carrington et al

27. 2b. The behavior of BaFe2(As1-xPx)2, Tc =30K Y. Matsuda et al BaFe(AsP) (BaK)FeAs Consistent with line nodes

28. 2c. Residual term in c-axis thermal conductivity of overdoped Co-Ba122 a-axis conductivity c-axis conductivity J-Ph. Reid et al

29. Back to a simple reasoning Problem: how to get rid of an intra-band Coulomb repulsion? Pnictides Cuprates Intra-band repulsion does not cancel and has to be overtaken by a (p,p) interaction Coulomb repulsion cancels out, only d-wave, (p,p)interaction matters

30. u4 electron FS A toy model: one hole and one electron FSs. Pairing interactions: u3 u4 Intra-band repulsion u4 hole FS Pair hopping (p,p) interaction s+- superconductivity, a simple RPA If the intra-band repulsion (u4) is stronger than the pair hopping (u3), the pairing interaction is repulsive

31. How to overcome intra-pocket Coulomb repulsion is the most essential part of the theory of itinerant superconductivity in Fe-pnictides

32. I. Pnictides are multi-orbital systems Electronic Structure: a zoo of p- and d-states bands 10 Fe d-bands in the window of +- 2 eV 12 O and As p-bands from -6 eV to -2 eV La f-bands at around -3 eV L. Boeri, O.V. Dolgov, and A.A. Golubov, PRL 101, 026403 (2008) Strong hybridization of all Fe-orbitals

33. What multi-orbital/multi-band structure means for our story? • Interactions between low-energy fermions are dressed by orbital • coherence factors and in general have strong angular dependence. Exercise in trigonometry with s-wave interactions: Effective intra-band interaction: Effective inter-band interaction: (previously we only had u3) This is still s-wave!

34. Solve three coupled BCS equations for the gaps: When is zero, the solution for Tc exists only for u3>u4 When is non-zero, the solution exists for arbitrary u3/u4 and for arbitrary sign and magnitude of , but the gap along electron FS has nodes for u3>u4.

35. Superconducting phase diagram s+- gap with the nodes on electron FS d-wave gap with the nodes on both FS s+- gap with no nodes 1 Coulomb repulsion is the strongest – the s+- gap with the nodes along electron FS is most likely scenario

36. How can the system develop a no-nodal gap (still of s+- symmetry) ? SmOFeAs

37. RG helps: u4 and u3 are bare interactions,at energies of a bandwidth For SC we need interactions at energies smaller than the Fermi energy EF ~ 0.1 eV W ~3-4 eV | | E 0 Couplings flow due to renormalizations by particle-particle and particle-hole bubbles

38. We know this story for conventional (phonon) superconductors EF ~ W wD 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 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)

39. One-loop parquet RG Intra-band repulsion u4 Pair hopping (p,p) interaction Inter-band density-density and exchange interaction u3 is pushed up by u1 , which gives rise to SDW SDW u0L If the tendency towards SDW is strong, u3 becomes larger than u4, leading to an s+- superconductivity with no-nodal gap

40. Superconducting phase diagram s+- gap with the nodes on electron FS d-wave gap with the nodes on both FS s+- gap with no nodes 1 Less SDW fluctuations If RG renormalization is strong, Coulomb interaction is overshadowed, and the s+- gap may have no nodes along the electron FS LaFeOP, Overdoped FeAs Underdoped 1111, 122 FeAs

41. The role of spin fluctuations SC sf Spin-fluctuation exchange is an additional dynamical interaction, which acts in parallel with the pair hopping. The real issue is what sets the upper cutoff for the pairing: the scale at which u3 =u4, or the dynamics of the spin-fluctuatioon exchange

42. Interplay between magnetism and superconductivity We can re-write these as equations for SDW, CDW, and SC vertices - - Interactions in all channels grow

43. One-loop RG Flow – all channels SDW with real order parameter Above EF CDW with imaginary order parameter O(6) fixed point: 3 for SDW, 2 for SC, 1 for CDW Extended s-wave Lower boundary for parquet RG is the Fermi energy, EF

44. Below EF – decoupling between SDW and SC channels For a perfect nesting, whichever vertex is larger at EF, wins

45. Perfect nesting – SDW wins Non-perfect nesting –SDW vertex remains the strongest, but the SDW instability is cut, and s+- SC wins

46. Either first-order transition between SDW and SC states, or co-existence, depending on parameters depending on the degree of ellipticity of electron FSs doping doping Fernandes, Schmalian, et al, Vorontsov, Vavilov, AC

47. How important is the fact that there are 5 bands and the orbital structure changes along the FS? Detailed studies: Mazin & Schmalian Graser, Maier, Hirschfeld, Scalapino Thomale, Platt, Hanke, Bernevig. D-H Lee, Vishvanath, Honerkamp, Benfatto, Grilli, Kuroki, Imada… At least 2 hole and two electron FSs Coldea et al, dHvA additional 3D FSs

48. These extra features give rise to some qualitative changes, but do not change the overall picture of s+- pairing IIa. RG for 2 hole and 2 electron FSs more parameters, more equations 2 hole 2 electron FSs 1hole 1 electron FSs Thomale et al Maiti, AC Still, SC vertex changes sign under RG

49. Summary: the phase diagram: Angle dependence of the interaction s+- gap with the nodes on electron FS s+- gap with no nodes Position depends on interactions, FS geometry, etc… Coulomb repulsion 1 Less SDW fluctuations LaFeOP, Overdoped FeAs Underdoped 1111, 122 FeAs

50. Conclusions: Fe-pnictides are itinerant systems, no evidence for Mott physics 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.