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)

Cuprates

Iron Pnictides

New families coming: A1-xA’xFe2As2, LiFeAs,

Sr1-xLaxFeAsF

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

Iron Pnictides: chemical composition

RE3+ – TM2+ – O2- – Pn3-

AT2+ - 2Fe 2+ - 2As 3- A1+ - Fe 2+ -As3-

Sr2+-Fe2+-As3--F1-

Pnictides: Crystal structure

High Tc SC based on As-Fe layers

TM2+ – Pn3- – (RE3+, A2+) – O2-

TM2+ – Pn3- – (RE3+, B4+) – O2-

TM2+ – Pn3- – RE3+ – (O2-, F1-)

TM2+ – Pn3- – RE3+ – O2- (1 - )

h+

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:

Phase diagram of the Iron Pnictides

J. Zhao, et al. arXiv:0806.2528

Phase diagram of the cuprates

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

Naive countingdxy

dxz, dyz

d3z2-r

2

dx2-y

2

dxy

dxz, dyz

d3z2-r

2

dx2-y

2

d iron orbitals in a squashed tetrahedral environment

adding Hund’s rule Multiorbital and

Spin 2

Introducing interactions:U -> intraorbital repulsionU’ -> interorbital repulsionJ -> Hund’s coupling

In cuprates we just have one orbital (dx2-y

2) and 1 electron!

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

First principle calculations

S. Lebègue, et al., Phys. Rev. B’07Iron moment = 2.3 ,

Z. P. Yin, et al. Phys. Rev. Lett’08

2D Fermi surface in ReOFeAsin 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?

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 forLaOFeAs, C. Cruz et al., Nature’08Iron moment = 0.36 : VERY SMALL!

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 forLaOFeAs, C. Cruz et al., Nature’08Iron moment = 0.36 : VERY SMALL!

QP peakFermi surface

The parent compound is a METAL. Pseudogap? So far when Pn=As

Experiments: Superconducting phase

G. Li, et al. Phys. Rev. Lett’08

Bulk SC in Ba0.6K0.4Fe2As2

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 Ba0.6K0.4Fe2As2

G. Li, et al. Phys. Rev. Lett’08

Bulk SC in Ba0.6K0.4Fe2As2

TheoryCONTROVERSY

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

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!

Our work: Distortion of the tetrahedron in iron

pnictides

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

Fe

Experimental fact: properties of LaOFeP and

LaOFeAs are very differentNeither structural nor magnetic transition, lower Tc

Structural and magnetic transition, higher Tc

T.M. McQueen, et al. Phys. Rev. B’08

Angle dependence in First-principle calculations: LDA

V. Vildosola, e al. arXiv:0806.2528

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

The Fe crystal field environment The Fe crystal field environment due to As atoms is nearly due to As atoms is nearly tetrahedraltetrahedral θtetra=π/2-54.7º and the order of the energy levels is

But:

How varies the hopping –the How varies the hopping –the band, the DOS, the FS- when band, the DOS, the FS- when varying the angle?varying the angle?

T.M. McQueen, et al. arXiv:0805.2149

deg

deg

This angle varies!

Iron - environment

Tight-binding for two levels, dxz and dyz, angle-dependence of the hopping

following Slater-Koster

DOS+BANDS

Flat band

Topology of the energy levels

Squashed Eminus

Squashed Eplus

Elongated EminusRegular Eminus

Regular Eplus Elongated Eplus

Black level-> Fermi surface at x=0

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

the angle for the low energy properties.the angle for the low energy properties. MJ Calderón, B.V,, E. Bascones, arXiv:0810.0019