1. A new class of high temperature superconductors: “Iron pnictides” Belén Valenzuela Instituto de Ciencias Materiales de Madrid (ICMM-CSIC) In collaboration with: María J. Calderón and Elena Bascones (ICMM-CSIC)

2. Cuprates

3. Iron Pnictides New families coming: A 1-x A’ x Fe 2 As 2, LiFeAs, Sr 1-x La x FeAsF

4. Index: -What is a pnictide? -Crystal structure & Phase diagram -Building a Hamiltonian: First principle calculations -Experimental description of the parent compound -Experimental description of the superconducting phase -Theory -Our work

5. Iron Pnictides: chemical composition RE 3+ – TM 2+ – O 2- – Pn 3- AT 2+ - 2Fe 2+ - 2As 3- A 1+ - Fe 2+ -As 3- Sr 2+ -Fe 2+ -As 3- -F 1-

6. Pnictides: Crystal structure High Tc SC based on As-Fe layers TM 2+ – Pn 3- – (RE 3+, A 2+ ) – O 2- TM 2+ – Pn 3- – (RE 3+, B 4+ ) – O 2- TM 2+ – Pn 3- – RE 3+ – (O 2-, F 1- ) TM 2+ – Pn 3- – RE 3+ – O 2- (1 -  ) h+h+ e-e- e-e- e-e- a = b ~ 3.96 Å c ~ 8.5 Å Cuprates crystal structure: High Tc SC based on Cu-O layers Doping possibilities:

7. Phase diagram of the Iron Pnictides J. Zhao, et al. arXiv:0806.2528 Phase diagram of the cuprates

8. Building a hamiltonian for Iron Pnictides Effective model: iron square lattice with two atoms per unit cell, Fe in an As-tetrahedral environment Fe Top As Bottom As

9. Naive counting d xy d xz, d yz d 3z 2 -r 2 d x 2 -y 2 d xy d xz, d yz d 3z 2 -r 2 d x 2 -y 2 d iron orbitals in a squashed tetrahedral environment adding Hund’s rule Multiorbital and Spin 2 Introducing interactions: U -> intraorbital repulsion U’ -> interorbital repulsion J -> Hund’s coupling In cuprates we just have one orbital ( d x 2 -y 2 ) and 1 electron!

10. First principle calculations S. Lebègue, et al., Phys. Rev. B’07 DOS in LaOFeP from LDA 4p P 3d Fe LaO FeP 3d Fe plays the main role in the low energy physics (though very strong hibridization with P). Semimetal

11. First principle calculations S. Lebègue, et al., Phys. Rev. B’07 Iron moment = 2.3  , Z. P. Yin, et al. Phys. Rev. Lett’08 2D Fermi surface in ReOFeAs in the folded Brillouin zone 3D Fermi surface in LaOFeP from LDA: All the d-orbitals of the iron are involved Raghu et al, PRB’08 2D hole pockets 2D electron pockets Controversy in Density Functional Theory (DFT) -> Strong or weak coupling?

12. Experiments: Parent compound It suffers a structural (from tetragonal to orthorhombic or monoclinic) at Tc~150K and a magnetic transition at Tc~134K (long range stripe antiferromagnetic phase). Neutron diffraction data for LaOFeAs, C. Cruz et al., Nature’08 Iron moment = 0.36   : VERY SMALL!

13. Experiments: Parent compound ARPES for LaOFeP D. H. Lu, et al., arXiv: 0807.2009 It suffers a structural (from tetragonal to orthorhombic or monoclinic) at Tc~150K and a magnetic transition at Tc~134K (long range stripe antiferromagnetic phase). Neutron diffraction data for LaOFeAs, C. Cruz et al., Nature’08 Iron moment = 0.36   : VERY SMALL! QP peak Fermi surface The parent compound is a METAL. Pseudogap? So far when Pn=As

14. Experiments: Superconducting phase G. Li, et al. Phys. Rev. Lett’08 Bulk SC in Ba 0.6 K 0.4 Fe 2 As 2

15. Experiments: Superconducting phase H. Ding et al., Europhysics Letters’2008, Agrees with optical conductivity experiments Controversy: nodal gap? (d-wave, s-wave, extended s-wave) Multiband superconductivity? Intraorbital or interorbital? SC gap in Ba 0.6 K 0.4 Fe 2 As 2 G. Li, et al. Phys. Rev. Lett’08 Bulk SC in Ba 0.6 K 0.4 Fe 2 As 2

16. Theory CONTROVERSY Yildirim, Phys. Rev. Lett’08 Weak coupling view: SDW instability at the Fermi surface: nesting Strong coupling view: localized moments Frustrated magnetic system, metal close to a Mott transition Controversy for both views: How many orbitals are necessary to explain the low energy properties? Korshunov & Eremin arXiv:0804.1793 U<W U>W

17. Summary -> A new class of layered high temperature superconductors have been discovered this year: iron pnictides Experiments: -> The metallic parent compound suffers a structural (from tetragonal to monoclinic or orthorhombic) and a magnetic transition (to stripe antiferromagnetism). These transitions might be related. -> Doping the system both the antiferromagnetic phase and the structural distortion disappears -> Pseudogap? -> Order of the superconducting parameter: CONTROVERSY (d-wave, s-wave, extended s-wave, one gap, multiband gap -interband or intraband-…) -> Mechanism? Spin fluctuations, orbital fluctuations, phonons… Theory: 1. Controversy between strong and weak coupling views 2. Multiorbital character: How many orbitals are necessary to understand these compounds? ORIGINAL FROM THESE COMPOUNDS: THEY ARE EXTREMELY SENSITIVE TO STRUCTURAL MANIPULATIONS!

18. Our work: Distortion of the tetrahedron in iron pnictides

19. Experimentally and in first principle calculations the As-tetrahedral environment of the iron, controlled by the angle of the Fe-Pn bond to the vertical (θ), is crucial for the superconducting, magnetic and structural properties of the iron pnictides. θ As Fe

20. Experimental fact: properties of LaOFeP and LaOFeAs are very different Neither structural nor magnetic transition, lower Tc Structural and magnetic transition, higher Tc T.M. McQueen, et al. Phys. Rev. B’08

21. Angle dependence in First- principle calculations: LDA V. Vildosola, e al. arXiv:0806.2528

22. Angle dependence in experiments J. Zhao, e al. arXiv:0806.2528 Angle depends on doping Angle related with electron correlation. For the regular tetrahedron the highest Tc C.H. Lee, e al., J. Phys. Soc. Jpn’08

23. The Fe crystal field environment due to As atoms is nearly tetrahedral tetrahedral θ tetra =π/2-54.7º and the order of the energy levels is But: How varies the hopping –the band, the DOS, the FS- when varying the angle? How varies the hopping –the band, the DOS, the FS- when varying the angle? T.M. McQueen, et al. arXiv:0805.2149 deg This angle varies! Iron - environment

24. Tight-binding for two levels, dxz and dyz, angle-dependence of the hopping following Slater-Koster

25. DOS+BANDS Flat band

26. Topology of the energy levels Squashed Eminus Squashed Eplus Elongated Eminus Regular Eminus Regular Eplus Elongated Eplus Black level-> Fermi surface at x=0

27. Summary of our work We have studied the dependence of the angle of the Fe- Pn bond to the vertical (θ) for the two band model with the two orbitals dxz and dyz within the Slater-Koster formalism. As a result: -The model is extremely sensitive to the angle: important for weak coupling models based on nesting properties and for strong coupling models based on superexchange. -The hoppings strongly depend on angle. -There is a robust flat band for the regular tetrahedron. As a consequence, there is a change in the topology of the energy levels for the squashed, regular and elongated tetrahedron. -When adding more bands the flat band loses the flat character but the system remains very sensitive to the angle for the low energy properties. MJ Calderón, B.V,, E. Bascones, arXiv:0810.0019