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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 !