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Electronic band structure of
ferro-pnictide superconductors
(FPS)
Alexander Kordyuk
IFW Dresden & IMP Kiev
FPS'11
Zvenigorod, 03.10.2011
Authors and Collaborations
S. V. Borisenko A. N. Yaresko A. Varykhalov
D. V. Evtushinsky D. S. Inosov E. Rienks
V. B. Zabolotnyy A. V. Boris R. Follath
T. K. Kim G. L. Sun
D. L. Sun
I. Morozov V. Hinkov H. Q. Luo
S. Aswartham C. T. Lin Z. S. Wang
S. Wurmhel B. Keimer H. H. Wen
G. Behr
C. Hess
R. Hübel
A. Koitzsch
M. Knupfer
B. Büchner
DFG Research Unit 538
and priority program
SPP 1458
Plan
• ARPES on FPS
• Band structure of 111 and 122
• Which electrons do superconductivity
• ... and why?
Photoelectric effect + electron analyser
ARPES Image
energy
angle / momentum
ARPES Image → ARPES Space
Momentum-energy space
EK
ky
kx
TiSe2
95
Kinetic energy (eV)
94
93
92
91
-1 0 -5 0 5 10 15
Momentum
Fermi surface (energy distribution) map
TiSe2 EK
ky
kx
Surface vs Bulk
Bi2Se3
Iron-based superconductors
Hai-Hu Wen and Shiliang Li, Annu. Rev. Condens.Matter Phys. 2011
Iron-based superconductors
11
FeSe 111 122
FeTe LiFeAs BaFe2As2
1111
LaFeAsO
Paglione & Greene, Nat. Phys. (2010)
122: truncated square tiling
M Г
X
Z
Z=
Band structure of 122 (BFA)
Yaresko 2010
Band structure of 122 (BFA)
Yaresko 2010
Band structure of FPS
Yaresko 2010
Iron-based superconductors
11
FeSe 111 122
FeTe LiFeAs BaFe2As2
1111
LaFeAsO
ARPESable Paglione & Greene, Nat. Phys. (2010)
Phase diagrams
H.Luetkens et al. Nature Mat. 2009
H.-H.Wen & S.Li Annu. Rev. Cond. Mat. S.Nandi et al. PRL 2010
Phys. 2011
N.Katayama et al. arXiv:1003.4525 Y.J.Yan et al. arXiv:1104.4941 Basov & Chubukov Nature Phys. 2011
Phase diagrams
111
S.Jiang et al. J.Phys.Cond.Matt. 2009 X.C.Wang et al. High
Pressure Research 2011
111
LiFeAs (Tc = 18 K, non-magnetic)
NaFeAs (Tc = 9-26 K, TAF = 40 K)
Perfectly ARPESable LiFeAs
1. Superconducting with Tc = 18 K but non-magnetic…
2. Stoichiometric = impurity clean.
3. Perfectly two-dimensional Fe-3dxy band well separated from
other bands: easy to analyse its fine structure.
4. Cleaves between the two Li layers => non-polar surface.
LiFeAs: band structure
Borisenko PRL 2010
LiFeAs: band structure
dxy
dxz
dyz
Graser et al. New J. Phys. 2009
Three orbital model
P.A.Lee & X.-G.Wen PRB 2008
LiFeAs: band structure
0.5
LDA
Calculated energy (eV)
0.0
-0.5
Experimental energy (eV)
0.1
0.0
• 3 times renormalized;
-0.1
• dxy band is 60 (bare 180) meV higher:
-0.3 -0.2
no FS nesting;
ARPES • dxz/dyz bands are 40 (120) meV lower;
Γ X
• dxz/dyz bands are flattened or “pinned”
In-plane momentum
to the Fermi level.
Borisenko PRL 2010
Yaresko 2010
LiFeAs: renormalization
λ = λel + λph = 2 + 1.38
Kordyuk PRB 2010
LiFeAs: FS orbital character
dxy
dxz
dyz
122
hole doped
BaFe2As2 (BFA) ▪ Ba1-xKxFe2As2 (BKFA) ▪ KFA
Ba1-xNaxFe2As2 (BNFA)
122
electron doped
BFA ▪ Ba(Fe1-xCox )2As2 (BFCA)
122
isovalent doping
BaFe2(As1-xPx )2 (BFAP)
H. Shishido et al. PRL 2010
Fermi surface of BKFA
Mazin & Schmalian 2009
Ding EPL 2008
Tesanovic Physics 2009 Shimojima Science 2011 Hu & Ding arXiv:1107.1334
Fermi surface of BKFA
Fermi surface of BKFA
V. Zabolotnyy Nature 2009, Phys C 2009
V. Zabolotnyy Nature 2009, Phys C 2009
Propeller FS in 122
Ba(Fe1-xCox )2As2 Ba1-xKxFe2As2 Ba1-xNaxFe2As2
ω = –90 meV, hv = 80 eV ω = 0, hv = 80 eV ω = 0, hv = 80 eV
Evtushinsky 2010
Calculated FC of BFA - BKFA Г M
Yaresko, Zabolotnyy 2011
BKFA: exp & calc
Yaresko, Zabolotnyy 2011
Calculated BFA band structure
renormalized and shifted by 76 meV
Г X Г T P T M X M
Yaresko, Zabolotnyy 2011
dxz + dyz
dxy
Yaresko 2010
Experimental energy (eV) Calculated energy (eV)
-0.3 -0.2 -0.1 0.0 0.1 -0.5 0.0 0.5
Γ
LDA
ARPES
In-plane momentum
X
BKFA: band structure
BKFA: Fermi surface and gaps
D. Evtushinsky PRB 2009, NJP 2009
dxy
Δ correlates with the orbital composition:
dxz
Δ = 3–4 meV for 3dxy and 3dz2
dyz Δ = 10.5 meV for 3dxz/yz.
D. Evtushinsky 2011
BFAP: node or small gap?
Y. Zhang et al. arXiv:1109.0229
KFA: hole-like Fermi surfaces
T. Yoshida et al. arXiv:1007.2698v2
FS‘s of iron-based superconductors
D. Evtushinsky 2011
FS‘s of iron-based superconductors
D. Evtushinsky 2011
BFA: density of states
AxFe2Se2 (31K)
BFCA (26K)
LiFeAs (18K)
DOS
BFA
-0.2 -0.1 0 0.1 0.2
Binding energy (eV)
BFA: density of states
AxFe2Se2 (31K)
BKFA (38K)
BFCA (26K)
LiFeAs (18K)
DOS
BFA
-0.2 -0.1 0 0.1 0.2
Binding energy (eV)
Tc(density of states)?
Sadovskii, Kuchinskii, Nekrasov 2011
BFA: density of states
AxFe2Se2 (31K)
BKFA (38K)
Hole doped KFA
BFCA (26K)
LiFeAs (18K)
DOS
BFA
KFA (4K) ???
-0.2 -0.1 0 0.1 0.2
Binding energy (eV)
Generalized phase diagram
140
Ba(Fe1-xCox )2As2
120
100
KxFe2-ySe2
Temperature
80
Ba1-xKxFe2As2
60
40 KFe2As2 SDW
20
SC SC SC
0
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1
Extra electrons per Fe atom
dxz + dyz
KFA BKFA BFCA KFS
SC & SDW
Kopaev & Rusinov Phys. Let. A 1987…
SC & SDW
Kopaev & Rusinov Phys. Let. A 1987…
SC & SDW
Yaresko 2011
Conclusions
• The band structure of Fe-SC is well captured by LDA
but do not take it too literally. The calculated Fermi
surface is usually bad starting point for theory.
• Main contributors to SC are dxz,yz electrons and Tc
for different compounds seems to correlate with the
position of the Van Hove singuliarities (Lifshitz
transitions) for the xz- and yz-bands.
• Both the renormalization and SDW do increase the
DOS at the Fermi level for dxz,yz- electrons.
THANK YOU
