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Interplay between magnetism and superconductivity in Fe-pnictides

Interplay between magnetism and superconductivity in Fe-pnictides. Andrey Chubukov. University of Wisconsin. INFN, Frascati, July 14, 2011. Superconductivity:. Zero-resistance state of interacting electrons.

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Interplay between magnetism and superconductivity in Fe-pnictides

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  1. Interplay between magnetism and superconductivity in Fe-pnictides Andrey Chubukov University of Wisconsin INFN, Frascati, July 14, 2011

  2. Superconductivity: Zero-resistance state of interacting electrons Electrons (fermions) attract each other and form bound states (bosons) .Bound states condence (a’la Bose-Einstein condensation) and move fully coherently under the electric field.One needs to destroy a bound state to stop the current.

  3. Superconductivity

  4. A magnetic field is expelled from a superconductor(Meissner effect) Ideal diamagnetism

  5. Nobel Prize 1913 Superconductivity: discovery It all started in 1911! H. Kamerlingh Onnes Superconducting mercury (1911)

  6. BCS theory • If there is an attractive interaction between fermions, they always form a bound state and condense below a certain Tc p k -k -p • In conventional, low Tc superconductors, an • attractive interaction is provided by exchanging • phonons (lattice vibrations)

  7. Superconductivity: High-Tc Alex Muller and Georg Bednortz Nobel prize, 1987 105 publications

  8. What is so exciting about high Tc superconductors? 1. quasi-two dimensionality

  9. What is so exciting about high Tc superconductors? d-wave symmetry of the superconducting gap 2. Most likely, electron-electron interaction rather that electron-phonon interaction is responsible for the pairing kF

  10. What is so exciting about high Tc superconductors? 3. Parent compounds are Mott insulators and Heisenberg antiferromagnets superconductor Is antiferromagnetism related to superconductivity?

  11. Can we think about spin fluctuations as a new pairing glue? 0 0 0 0 Campuzano et al d-wave

  12. Can we think about spin fluctuations as a new pairing glue? Yes, we can No, the interaction is too strong, Mott physics determines everything

  13. Phase diagram of cuprates contains much more than just magnetism and superconductivity

  14. Can we think about spin fluctuations as a new pairing glue? Yes, we can No, the interaction is too strong, Mott physics determines everything 2007

  15. Iron-based superconductors #6- Iron-based Superconductors, which rivaled swine-flu for citations among scholars… Science Blockbuster of 2008

  16. Fe-Pnictide high temperature superconductors: 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 LaOFeP AFe2As2 (122) A = Ba, Sr, Ca LiFeAs (111) Fe(Se/Te) (11)

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

  18. 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

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

  20. Crystal structure LaFeAsO 2D Fe-As layers with As above and below a square lattice formed by Fe

  21. Cuprates Pnictides Parent compounds are insulators Parent compounds are metals

  22. Insulating behavior of parent compounds of the cuprates parent compounds (magnetic) Resistivity

  23. Metallic behavior of parent compounds of Fe pnictides TN Resistivity 0

  24. 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)

  25. 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)

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

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

  28. How about using the “analogy” with the cuprates and assume that the pairing is mediated by spin fluctuations Cuprates Fe-pnictides spin fluct. spin fluct. 0 sign-changing s-wave gap (s+-) d-wave gap (dx2-y2)

  29. Experiments are generally consistent with the sign-changing s+- gap

  30. S-wave 1a. Photoemission in 1111 and 122 FeAs Data on the hole Fermi surfaces NdFeAsO1-xFx BaFe2(As1-xPx)2 laser ARPES T. Shimojima et al Almost angle-independent gap (consistent with s-wave) T. Kondo et al.

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

  32. However, superconductivity only appears at a finite doping

  33. 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

  34. uee electron FS A 2-band toy model: one hole and one electron FSs. Pairing interactions: uhe uhh Intra-band repulsion uhh,uee uhh uee hole FS Pair hopping uhe uhe (p,p) interaction need l >0 for pairing BCS If intra-pocket repulsions uhh, uee are stronger than the pair hopping uhe, the pairing interaction is repulsive, ls1,2 <0 In general, uee uhh should be the largest interactions (uee uhh are Coulomb repulsions at a small momentum transfer )

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

  36. RG helps: uee and uhe 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 in particle-particle and particle-hole channels

  37. Peculiarity of Fe-pnictides: Renormalizations in particle-particle and particle-hole channels are logarithmically singular particle-particle channel – Cooper logarithm particle-hole cannel – logarithm due to nesting Then we can do parquet RG

  38. Five relevant couplings between low-energy fermions superconductivity Interaction within hole or electron band (Coulomb repulsion) = uhh = uee Interband forward and backward scattering magnetism (SDW) Interband pair hopping = uhe We need enhancement of u3 relative to u4, u5 for superconductivity superconductivity

  39. Particle-hole channel 1 loop RG Particle-hole channel Particle-particle channel

  40. One-loop parquet RG The fixed point: the pair hopping term u3 is the largest Over-screening: intraband interaction u4 changes sign and becomes attractive below some scale.

  41. We can re-write parquet RG equations as equations for density-wave and superconducting vertices Super- conductivity Spin-density wave Charge-density wave

  42. One-loop RG Flow – all channels nt) SDW with real order parameter Above EF CDW with imaginary order parameter (charge current) 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

  43. Below EF – decoupling between SDW and SC channels Whichever vertex is the larger at EF, wins

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

  45. In real systems, there are 2-3 hole and 2 electron Fermi surfaces more parameters, more equations 2 hole and 2 electron FSs 1 hole and 1 electron FSs Still, SC vertex changes sign under RG

  46. 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, once antiferromagnetic 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 strong variations along the two electron Fermi surfaces.

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

  48. THANK YOU

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