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

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.

Superconductivity

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

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

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

Superconductivity: High-T c 10 5 publications Alex Muller and Georg Bednortz Nobel prize, 1987

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

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

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

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

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

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

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

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

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 AFe 2 As 2 (122) A = Ba, Sr, Ca LiFeAs (111) Fe(Se/Te) (11)

Hideo Hosono, TITechFe-pnictides: May

LaFeAsO 1-x F x La 1-x Sr x FeAsO SmFeAsO 1-x F x CeFeAsO 1-x F x PrFeAsO 1-x F x NdFeAsO 1-x F x GdFeAsO 1-x F x SmFeAsO 1-x F x SmFeAsO 1-x GdFeAsO 1-x Gd 1-x Th x FeAsO DyFeAsO 1-x F x TbFeAsO 1-x F x Tb 1-x Th x FeAsO Ba 1-x K x Fe 2 As 2 Sr 1-x K x Fe 2 As 2 Eu 1-x La x Fe 2 As 2 Ca 1-x Na x Fe 2 As 2 Eu 1-x K x Fe 2 As 2 Li 1-x FeAs  -FeSe 1-x BaNi 2 P 2 LaO 1-x NiBi LaOFeP LaO 1-x F x FeP LaONiP  -FeSe SrNi 2 As 2 BaCo x Fe 2-x As 2 SrCo x Fe 2-x As 2 BaNi x Fe 2-x As 2 FeSe 0.5 Te T c (K) courtesy of J. Hoffman

Phase diagram: magnetism and superconductivity BaFe 2 (As 1-x P x ) 2 Fernandes et al Matsuda et al Luetkens et al

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

Cuprates Pnictides Parent compounds are metalsParent compounds are insulators

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

 Metallic behavior of parent compounds of Fe pnictides Metallic behavior of parent compounds of Fe pnictides TNTN Resistivity

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

NdFeAs(O 1-x F x ) (x=0.1) A. Kaminski et al. Hole pockets near (0,0) Electron pockets near (  ) dHVa ARPES LaFeOP A. Coldea et al, Ba 06 K 04 Fe 2 As 2 H. Ding et al. A. Kordyuk et al LiFeAs

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?

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

Cuprates 0 How about using the “analogy” with the cuprates and assume that the pairing is mediated by spin fluctuations sign-changing s-wave gap (s +- ) Fe-pnictides spin fluct. d-wave gap (d x2-y2 )

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

Almost angle-independent gap (consistent with s-wave) NdFeAsO 1-x F x 1a. Photoemission in 1111 and 122 FeAs T. Shimojima et al BaFe 2 (As 1-x P x ) 2 S-wave T. Kondo et al. Data on the hole Fermi surfaces laser ARPES

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

However, superconductivity only appears at a finite doping

Back to a simple reasoning Problem: how to get rid of an intra-band Coulomb repulsion? Cuprates Pnictides Coulomb repulsion cancels out, only d-wave,  interaction matters Intra-band repulsion does not cancel and has to be overtaken by a  interaction

hole FS u hh u he electron FS Intra-band repulsion u hh, u ee Pair hopping u he  interaction u ee If intra-pocket repulsions u hh, u ee are stronger than the pair hopping u he, the pairing interaction is repulsive, s 1,2 <0 Pairing interactions: A 2-band toy model: one hole and one electron FSs. In general, u ee u hh should be the largest interactions (u ee u hh are Coulomb repulsions at a small momentum transfer ) u hh u ee u he BCS need >0 for pairing

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

RG helps: u ee and u he are bare interactions at energies of a bandwidth For SC we need interactions at energies smaller than the Fermi energy E E F ~ 0.1 eV W ~3-4 eV | | 0 Couplings flow due to renormalizations in particle-particle and particle-hole channels

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

Five relevant couplings between low-energy fermions Interaction within hole or electron band (Coulomb repulsion) Interband forward and backward scattering Interband pair hopping = u hh = u ee = u he magnetism (SDW) superconductivity We need enhancement of u 3 relative to u 4, u 5 for superconductivity

Particle-particle channel Particle-hole channel 1 loop RG

One-loop parquet RG Over-screening: intraband interaction u 4 changes sign and becomes attractive below some scale. The fixed point: the pair hopping term u 3 is the largest

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

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

Below E F – decoupling between SDW and SC channels Whichever vertex is the larger at E F, wins

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

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

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

The behavior of BaFe 2 (As 1-x P x ) 2, Tc =30K The behavior of BaFe 2 (As 1-x P x ) 2, Tc =30K Y. Matsuda et al (BaK)FeAs BaFe(AsP) Consistent with line nodes in the superconducting gap.

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