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Xi Dai Institute of Physics(IOP), CAS Beijing, China

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

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Xi Dai Institute of Physics(IOP), CAS Beijing, China

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  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. 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: Takea non-interacting system as reference

  4. Using local density approximation in GDFT Generalized KS ansatz: Gutzwiller DFT Takea 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

  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+DMFT LDA+G LDA GGA 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+U LDA+DMFT (High T) LDA+G (T=0K) Two questions: 1. Fe-As distance? 2. SDW state and Magnetic moment?

  15. Structure: Building-block FeAs-layer

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

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

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

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

  20. 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)

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

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

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

  24. 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?

  25. Problems of LDA or GGA Problem (1): Fe-As position and bonding strength T. Fukuda, et. Al., arXiv:0808.0838 (cond-mat/0804.3355)

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 Problems of LDA or GGA Problem (2): The band width found by ARPES is 50% Narrower H. Ding et al, Unpublished

  27. Problem of LDA & GGA: 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)

  28. 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)

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

  30. LDA+G study for LaOFeP: As position

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

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

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

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

  35. The anisotropy in resistivity calculated by LDA+G

  36. 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

  37. Thank you !

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