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)

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

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

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

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

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

The flow chart of LDA+G

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

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

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

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

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

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?

Structure: Building-block FeAs-layer

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

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

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

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

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, 67002 (2008)

LaOFeAs: Fermi surface Nesting Success of LDA & GGA LaOFeAs: Fermi surface Nesting J. Dong, et.al., EPL, 83, 27006 (2008)

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)

Exp: Competing Orders X.H.Chen, et.al., P. Dai’s neutron Cond-mat/0807.3950 P. Dai’s neutron

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?

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:0808.0838 (cond-mat/0804.3355)

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

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/0804.2252)

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  X M  Z R A Z

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

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

The anisotropy in resistivity calculated by LDA+G

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 4. 3D FS, small anisotropy

Thank you !