A new class of high temperature superconductors:

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 A1-xAxFe2As2, LiFeAs,
Sr1-xLaxFeAsF
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
RE3 TM2 O2- Pn3-
AT2 - 2Fe 2 - 2As 3- A1 - Fe 2 -As3-
Sr2-Fe2-As3--F1-
6
Pnictides Crystal structure

• a b 3.96 Å
• c 8.5 Å

High Tc SC based on As-Fe layers
Doping possibilities
Cuprates crystal structure High Tc SC based on
Cu-O layers
7
Phase diagram of the Iron Pnictides
Phase diagram of the cuprates
J. Zhao, et al. arXiv0806.2528
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
dxy dxz, dyz d3z2-r2 dx2-y2
Introducing interactions U -gt intraorbital
repulsion U -gt interorbital repulsion J -gt
Hunds coupling
d iron orbitals in a squashed tetrahedral
environment
dxy dxz, dyz d3z2-r2 dx2-y2
adding Hunds rule
Multiorbital and Spin 2
In cuprates we just have one orbital (dx2-y2) and
1 electron!
10
First principle calculations
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
S. Lebègue, et al., Phys. Rev. B07
11
First principle calculations
3D Fermi surface in LaOFeP from LDA All the
d-orbitals of the iron are involved
2D Fermi surface in ReOFeAs in the folded
Brillouin zone
2D hole pockets
2D electron pockets
Raghu et al, PRB08
Controversy in Density Functional Theory (DFT) -gt
Strong or weak coupling?
S. Lebègue, et al., Phys. Rev. B07
Iron moment 2.3 mB , Z. P. Yin, et al. Phys.
Rev. Lett08
12
Experiments Parent compound
It suffers a structural (from tetragonal to
orthorhombic or monoclinic) at Tc150K and a
magnetic transition at Tc134K (long range stripe
antiferromagnetic phase).
Neutron diffraction data for LaOFeAs, C. Cruz et
al., Nature08 Iron moment 0.36 mB VERY
SMALL!
13
Experiments Parent compound
It suffers a structural (from tetragonal to
orthorhombic or monoclinic) at Tc150K and a
magnetic transition at Tc134K (long range stripe
antiferromagnetic phase).
The parent compound is a METAL. Pseudogap? So
far when PnAs
QP peak
Fermi surface
ARPES for LaOFeP D. H. Lu, et al., arXiv
0807.2009
Neutron diffraction data for LaOFeAs, C. Cruz et
al., Nature08 Iron moment 0.36 mB VERY
SMALL!
14
Experiments Superconducting phase
Bulk SC in Ba0.6K0.4Fe2As2
G. Li, et al. Phys. Rev. Lett08
15
Experiments Superconducting phase
Bulk SC in Ba0.6K0.4Fe2As2
SC gap in Ba0.6K0.4Fe2As2
G. Li, et al. Phys. Rev. Lett08
Controversy nodal gap? (d-wave, s-wave,
extended s-wave) Multiband superconductivity? Intr
aorbital or interorbital?
H. Ding et al., Europhysics Letters2008, Agrees
with optical conductivity experiments
16
Theory
CONTROVERSY
UltW
UgtW
Weak coupling view SDW instability at the Fermi
surface nesting
Strong coupling view localized
moments Frustrated magnetic system, metal close
to a Mott transition
Korshunov Eremin arXiv0804.1793
Controversy for both views How many orbitals are
necessary to explain the low energy properties?
Yildirim, Phys. Rev. Lett08
17
Summary
-gt A new class of layered high temperature
superconductors have been discovered this year
iron pnictides Experiments -gt 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. -gt Doping
the system both the antiferromagnetic phase and
the structural distortion disappears -gt
Pseudogap? -gt Order of the superconducting
parameter CONTROVERSY (d-wave, s-wave, extended
s-wave, one gap, multiband gap -interband or
intraband-) -gt 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 (?), is crucial for the
superconducting, magnetic and structural
properties of the iron pnictides.
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. B08
21
Angle dependence in First-principle calculations
LDA
V. Vildosola, e al. arXiv0806.2528
22
Angle dependence in experiments
For the regular tetrahedron the highest Tc
C.H. Lee, e al., J. Phys. Soc. Jpn08
Angle related with electron correlation.
Angle depends on doping
J. Zhao, e al. arXiv0806.2528
23
The Fe crystal field environment due to As
atoms is nearly tetrahedral ?tetrap/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?
deg
deg
This angle varies!
Iron - environment
T.M. McQueen, et al. arXiv0805.2149
24
Tight-binding for two levels, dxz and dyz,
angle-dependence of the hoppingfollowing
Slater-Koster
25
DOSBANDS
Flat band
26
Topology of the energy levels
Squashed Eplus
Regular Eplus
Elongated Eplus
Squashed Eminus
Regular Eminus
Elongated Eminus
Black level-gt Fermi surface at x0
27
Summary of our work

• We have studied the dependence of the angle of
  the Fe-Pn bond to the vertical (?) 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, arXiv0810.0019