1. UC Davis conference on electronic structure, June. 2009
LDA+Gutzwiller Method for Correlated Electron Systems:  Formalism and Its Application to Iron pnictides
Xi Dai
Institute of Physics(IOP), CAS
Beijing, China
Collabrators:
X.Y. Deng, G. T. Wang, G. Xu, H. J. Zhang
Zhong Fang (IOP)

2. Introduction to Gutzwiller density functional theory.
Contents
Introduction to Gutzwiller density functional theory.
(Problems of LDA)
2. LDA+Gutzwiller Method
Applications: Iron Pnictides
conclusions

3. The Kohn-Sham local density approximation
KS ansatz: Take a non-interacting system as reference

4. Using local density approximation in GDFT
Generalized KS ansatz: Gutzwiller DFT Take a system with on-site interaction as reference H=HLDA+HU-EDC

5. Gutzwiller wave-function for multi-orbital system
Γ: many body configurations on a single site.
Single band: 22=4
N-band: 22n

6. Gutzwiller Approximation: Generalizing to Multi-orbital

7. Bench mark Gutzwiller Aproximation on two-band
Hubbard model with DMFT+ED
Gutzwiller Vs
DMFT 7

8. The flow chart of LDA+G

9. Insufficiency of LDA for TMOs
Insulator
with
Long-range
ordering
Correlated-Metal or
MIT critical point
Metal
Ueff
LDA
GGA
LDA+DMFT
LDA+G
LDA+U

10. Example-1: Ground state of Fe
LDA+G
GGA
LDA
Deng, DX and FZ， EPL （2008）
J. H. Cho and M. Scheffler, PRB (1996)

11. Example-2: DFT results for Ni
LDA
Exp.
30% wider
X point problem
LDA＋G

12. Example-3: NaCoO2 LDA D.J. Singh, PRB (2000) ARPES
M.Z.Hasan, PRL (2004)
LDA+G
Wang, DX, FZ PRL (2008)

13. LDA+G covers: From Weakly correlated metals to
Strongly corrlated insulators (ordered state)
If q=1: HF limit is recovered (LDA+U)
If 0<q<1: Kinetic renormalization included
Same as DMFT for ground state!
Much cheaper than DMFT !
5 orbitals can be solved by 1-min on PC.
PRL (2008) for NaCoO2; EPL (2008) for details

14. Correlation In Iron Pnictides
Crucial
LaOFeAs:
Ueff=3~4eV, JH=0.6~1.0eV
Orbital fluctuation enhanced
La2CuO4
Ueff
Itinerant metal
MIT
Large U limit
LDA & GGA
LDA+DMFT (High T)
LDA+G (T=0K)
LDA+U
Two questions: 1. Fe-As distance?
2. SDW state and Magnetic moment?

16. Structure: Building-block FeAs-layer

17. Structure: Mainly 4 types
LaOFeAs (1111)
BaFe2As2 (122)
LixFeAs
FeSe

18. LDA Basic Electronic Structure: LaOFeAs Fe-3d As-4p O-2p Energy (eV) AΓ X M Γ Z R A Z
LDA

19. Basic Electronic Structure: LaOFeAs
Important: 5 orbitals/Fe are all involved
Fe2+: nd=6

20. Basic Electronic Structure: LaOFeAsFS
Strong anisotropy
Phonon
Weak e-p coupling
D. J. Singh & M. H. Du, PRL (2008).

21. Magnetic Phase Diagram of LaOMAs:
Success of LDA & GGA
Magnetic Phase Diagram of LaOMAs:
LaOMnAs:
AF1
Semiconductor
LaOCoAs:
FM Metal
Magnetic
instabilities??
G. Xu, et.al., EPL, 82, (2008)

22. LaOFeAs: Fermi surface Nesting
Success of LDA & GGA
LaOFeAs: Fermi surface Nesting
J. Dong, et.al., EPL, 83, (2008)

23. LaOFeAs: Stripe-type SDW (AF2)
Success of LDA & GGA
LaOFeAs: Stripe-type SDW (AF2)
J. Dong, et.al., EPL, (2008).
P. Dai, et.al., NATURE, (2008)

24. Exp: Competing Orders X.H.Chen, et.al., P. Dai’s neutron
Cond-mat/
P. Dai’s neutron

25. Basic Understanding from pure LDA:
From LDA or GGA:
1. Multi-orbital nature (Orbital DOF)
2. Magnetic instabilities (Spin DOF)
3. Lattice coupled to M (Lattice DOF)
Competing Orders is the Key!!!
Problems:
1. Spin: moment? SDW?
2. Orbital: selective?
3. Lattice: Fe-As distance?phonon?

26. Problem (1): Fe-As position and bonding strength
Problems of LDA or GGA
Problem (1): Fe-As position and bonding strength
T. Fukuda, et. Al.,
arXiv:
(cond-mat/ )

27. Problems of LDA or GGA H. Ding et al, Unpublished
Problem (2): The band width found by ARPES is 50% Narrower
H. Ding et al, Unpublished

28. Problem of LDA & GGA: Spatial or On-site Fluctuation? SDW
Problem (3): Magnetic Solution & Moment
SDW
M = 0.3~0.4 μB
From exp.
Spatial or On-site
Fluctuation?
T. Yildirim., et.al.,
(cond-mat/ )

29. Other evidence of strong correlation effects in Iron Pnictides
Large Specific heat coefficient in FeTe (arXiv: )
Incoherent spectral weight in optical conductivity
(N.L. Wang et al, unpublished)
Satellite peaks in core level spectra(H. Ding et al unpublished)

30. LDA+G study for LaOFeAs: As position
J is crucial !!

31. LDA+G study for LaOFeP: As position

32. LDA+G study for LaOFeAs: band-narrowing
Renormalization: about factor of 2
consistent with ARPES

33. LDA+G study for LaOFeAs: band-narrowing
A  X M  Z R A Z

34. LDA+G study for LaOFeAs:
Crystal field is suppressed!
Orbital Fluctuation is enhanced!
This explains why J is crucial!

35. The appearance of 3D FS
LaOF0.1Fe0.9As
Ba0.6K0.4Fe2As2

36. The anisotropy in resistivity calculated by LDA+G

37. 2. Phonon frequency is soften by 30% 3. Band-width renormalization
Conclusions:
Conclusions:
U = 3 ~ 4 eV
J = 0.6 ~1 eV  Crucial
Fe-As distance solved!
LaOFeAs, LaOFeP, BaFe2As2
2. Phonon frequency is soften by 30%
3. Band-width renormalization
factor of 2, orbital fluctuation
D FS, small anisotropy

38. Thank you !