xi dai institute of physics(iop), cas beijing, china
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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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)
UC Davis conference on electronic structure, June. 2009
Contents
1. Introduction to Gutzwiller
density functional theory.
(Problems of LDA)
2. LDA+Gutzwiller Method
3. Applications: Iron Pnictides
4. conclusions
The Kohn-Sham local density approximation
KS ansatz: Take a non-interacting system as reference
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Using local density approximation in GDFT
Generalized KS ansatz: Gutzwiller DFT Take a system with on-site interaction as reference H=HLDA+HU-EDC
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Gutzwiller wave-function for multi-orbital system
Γ: many body configurations on a single site.
Single band: 22=4
N-band: 22n
Gutzwiller Approximation:
Generalizing to Multi-orbital
∑ ∑∑ −+Γ+ΓΓ=Γ
+
βα ασασασασββααβα με
ji iiii
iijjiijieff nd
UqCCqtH
,
0
,
* )()(2
)()(
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Bench mark Gutzwiller Aproximation on two-band
Hubbard model with DMFT+ED
GutzwillerVsDMFT
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The flow chart of LDA+G
Insufficiency of LDA for TMOs
InsulatorwithLong-range ordering
Correlated-Metal orMIT critical point
Metal
Ueff
LDAGGA
LDA+ULDA+DMFTLDA+G
LDA GGA
J. H. Cho and M. Scheffler, PRB (1996)
Example-1: Ground state of Fe
LDA+GDeng, DX and FZ , EPL ( 2008)
Exp. LDA
Example-2: DFT results for Ni
1. 30% wider
2. X point problem
LDA + G
LDA
D.J. Singh, PRB (2000)ARPES
M.Z.Hasan, PRL (2004)
Example-3: NaCoO2
LDA+G
Wang, DX, FZ PRL (2008)
LDA+G covers:From Weakly correlated metals to Strongly corrlated insulators
(ordered state)
If 0<q<1: Kinetic renormalization included
If q=1: HF limit is recovered (LDA+U)
)2
1( −∝ αα nV
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
Correlation In Iron Pnictides
Ueff
LDA & GGA
Itinerant metal Large U limit
LDA+U
MIT
LDA+DMFT (High T)LDA+G (T=0K)
La2CuO4
LaOFeAs:Ueff=3~4eV, JH=0.6~1.0eVOrbital fluctuation enhanced
Two questions: 1. Fe-As distance? 2. SDW state and Magnetic moment?
Crucial
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Structure: Building-block FeAs-layer
Structure: Mainly 4 types
LaOFeAs (1111) BaFe2As2 (122)
LixFeAs FeSe
Basic Electronic Structure: LaOFeAs
MΓ X ZΓ R A ZA
En
erg
y (e
V)
Fe-3d
As-4p
O-2p
LDA
Basic Electronic Structure: LaOFeAs
Important: 5 orbitals/Fe are all involved
Fe2+: nd=6
Basic Electronic Structure: LaOFeAs
D. J. Singh & M. H. Du, PRL (2008).
FS
Strong anisotropy
Phonon
Weak e-p coupling
Success of LDA & GGA
Magnetic Phase Diagram of LaOMAs:
G. Xu, et.al., EPL, 82, 67002 (2008)
LaOMnAs:AF1Semiconductor
LaOCoAs:
FM Metal
Magnetic
instabilities??
Success of LDA & GGA
LaOFeAs: Fermi surface Nesting
J. Dong, et.al., EPL, 83, 27006 (2008)
Success of LDA & GGA
LaOFeAs: Stripe-type SDW (AF2)
J. Dong, et.al., EPL, (2008). P. Dai, et.al., NATURE, (2008)
Exp: Competing Orders
P. Dai’s neutron X.H.Chen, et.al.,
Cond-mat/0807.3950
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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?
Problems of LDA or GGA
Problem (1): Fe-As position and bonding strength
(cond-mat/0804.3355)
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T. Fukuda, et. Al.,arXiv:0808.0838
Problems of LDA or GGA
Problem (2): The band width found by ARPES is 50% Narrower
H. Ding et al, Unpublished
Problem of LDA & GGA:
Problem (3): Magnetic Solution & Moment
T. Yildirim., et.al.,
(cond-mat/0804.2252)
SDW
M = 0.3~0.4 μB
From exp.
Spatial or On-site
Fluctuation?
Other evidence of strong correlation effects in Iron Pnictides
•Large Specific heat coefficient in FeTe (arXiv:0811.1489)
•Incoherent spectral weight in optical conductivity (N.L. Wang et al, unpublished)
•Satellite peaks in core level spectra(H. Ding et al unpublished)
LDA+G study for LaOFeAs: As position
J is crucial !!
LDA+G study for LaOFeP: As position
LDA+G study for LaOFeAs: band-narrowing
Renormalization: about factor of 2
consistent with ARPES
LDA+G study for LaOFeAs: band-narrowing
A Γ X M Γ Z R A Z
LDA+G study for LaOFeAs:
Crystal field is suppressed!
Orbital Fluctuation is enhanced!
This explains why J is crucial!
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Ba0.6K0.4Fe2As2LaOF0.1Fe0.9As
The appearance of 3D FS
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The anisotropy in resistivity calculated by LDA+G
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Conclusions:
U = 3 ~ 4 eVJ = 0.6 ~1 eV Crucial
Conclusions:
1. Fe-As distance solved! LaOFeAs, LaOFeP, BaFe2As22. Phonon frequency is soften by 30%3. Band-width renormalization factor of 2, orbital fluctuation4. 3D FS, small anisotropy
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Thank you !