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Dynamical Mean Field Theory (DMFT) of correlated solids.

Dynamical Mean Field Theory (DMFT) of correlated solids. G.Kotliar Physics Department Center for Materials Theory Rutgers University. Collaborators: K. Haule (Rutgers), S. Savrasov (UC Davis). Gordon Research Conference on Solid State Chemistry II.

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Dynamical Mean Field Theory (DMFT) of correlated solids.

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  1. Dynamical Mean Field Theory (DMFT) of correlated solids. G.Kotliar Physics Department Center for Materials Theory Rutgers University. Collaborators: K. Haule (Rutgers), S. Savrasov (UC Davis) Gordon Research Conference on Solid State Chemistry II September 2-7 (2007) Magdalen College Oxford United Kingdom

  2. Outline • 1]Introduction to DMFT ideas. • 2]Application to elemental actinides, what is valence in a correlated solid ? • 3]Application to cobaltates, why are correlation stronger near a band insulator than near a Mott insulator? [C. Delmas talk A.Maignan talk] • Central theme, localization-delocalization ! • 4]Application to 115’s and the tale of multiple hybridization gaps. [F. Steglich talk]

  3. Correlated Electron Systems Pose Basic Questions in CMT • FROM ATOMS TO SOLIDS • How to describe electron from localized to itinerant ? • How do the physical properties evolve ?

  4. DMFT Spectral Function Photoemission and correlations e • Probability of removing an electron and transfering energy w=Ei-Ef, and momentum k f(w) A(w, K) M2 n n Angle integrated spectral function 8

  5. DMFT approximate quantum solid as atom in a medium 10

  6. Spectra=- Im G(k,w) Self consistency for V and e (GW) DFT+DMFT: determine H[k] and density and S self consitently from a functional and obtain total energies. 12

  7. Summary: part 1 Spectral function in DMFT analogous to density in DFT Self consistent Impurity problem, natural language to describe localization/delocalization phenomena. combines atomic physics and band theory Systematically improvable, cluster DMFT Recent progress in implementation • Gabriel Kotliar and Dieter Vollhardt, Physics Today 57, 53 (2004). • A. Georges, G. Kotliar, W. Krauth, and M. Rozenberg, Rev. of Mod. Phys. 68, 13-125 (1996). • G. Kotliar, S. Savrasov, K. Haule, V. Oudovenko, O. Parcollet, and C. Marianetti, Rev. of Mod. Phys. 78, 000865 (2006).

  8. Mott transition across the actinides. B. Johansson Phil Mag. 30,469 (1974)] Mott Transition d Pu a d a after G. Lander, Science (2003) and Lashley et. al. PRB (2006).

  9. Pu phases: A. Lawson Los Alamos Science 26, (2000) GGA LSDA predicts d Pu to be magnetic with a large moment ( ~5 Bohr). Experimentally Pu is not magnetic. [PRB 054416(2005). Valence of Pu is controversial.

  10. C11 (GPa) C44 (GPa) C12 (GPa) C'(GPa) Theory 34.56 33.03 26.81 3.88 Experiment 36.28 33.59 26.73 4.78 DMFT Phonons in fcc d-Pu ( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003) (experiments from Wong et.al, Science, 22 August 2003)

  11. Curie-Weiss Tc Photoemission of Actinides alpa->delta volume collapse transition F0=4,F2=6.1 F0=4.5,F2=7.15 F0=4.5,F2=8.11 Curium has large magnetic moment and orders antif Pu does is non magnetic.

  12. What is the valence in the late actinides ?

  13. Summary part 2 • Modern understanding of the Mott transition across the actinde series (B. Johanssen) sheds light on the physics of actinides. • Important role of multiplets. Pu is non magnetic and mixed valent element mixture of f6 and f5 • f electrons are localized in Cm f7 K. Haule and J. Shim Ref: Nature 446, 513, (2007)

  14. DMFT study of Nax CoO2

  15. Foo et.al. PRL 247001

  16. CoO2 NaCoO2

  17. Assume Na patterns of Zandbergen et. al.PRB 70 024101 C. A. Marianetti and G. Kotliar Phys. Rev. Lett. 98, 176405 (2007) . A

  18. DMFT calculations with and without disorder U=3 ev. C. A. Marianetti and G. Kotliar Phys. Rev. Lett. 98, 176405 (2007)

  19. x=.33 QP dispersion DMFT LDA

  20. References: part 3 • C. Marianetti, G. Kotliar, and G. Ceder, Nature Materials 3, 627 - 631 (2004). • C. A. Marianetti and G. Kotliar Phys. Rev. Lett. 98,176405 (2007) • C. Marianetti, K. Haule and O Parcollet cond-mat (2007) Alternative theory : low spin to high spin Khaliullin Phys. Rev. Lett. 96, 216404 (2006)

  21. Summary part 3 • What is the minimal model of the cobaltes ? • t2g orbitals + binary potential a see which results of the Li /Na vacancy . • Why are correlations stronger near a band insulator than near a Mott insulator ? • U < Uc2 , hole moves in a restricted space (where potential is low) and is strongly correlated. • DMFT calculations account for the Curie Weiss phase and the Fermi liquid phase

  22. Conclusion • DMFT as a technique, makes contact with experiments, total energies, phonons, photoemission, ARPES,optics,…thermopower…..neutron scattering ….. • Concepts, atom in a quantum medium, Weiss field, local spectral function, A(w), three peak structure,transfer of spectral weight , valence histogram, [bridges between atomic physics and band theory ] • Under constant development, but already gives some exciting results.

  23. Conclusions :chemistry brings out different aspects of localization delocalization physics. • Actinides, phonons, role of multiplets, spectral signatures, Pu as mixed valent metal. • Cobaltates, key role of inhomogeneities bringing correlations near a (correlated) insulator. DMFT treatment of an alloy. • 115’s delocalization transition as a function of T. Spectral function as a coherence order parameters. Multiple hybridization gaps.

  24. Thanks! Conclusions :chemistry brings out different aspects of localization delocalization physics. • Acknowldegment. NSF-DMR. DOE-BES. • Collaborators:K. Haule, C. Marianetti, J. Shim, and S. Savrasov

  25. Ir In Ce In Ce In Crystal structure of 115’s CeMIn5 M=Co, Ir, Rh Tetragonal crystal structure IrIn2 layer 3.27au 4 in plane In neighbors 3.3 au CeIn3 layer IrIn2 layer 8 out of plane in neighbors

  26.  CeRhIn5: TN=3.8 K;   450 mJ/molK2CeCoIn5: Tc=2.3 K;   1000 mJ/molK2; CeIrIn5: Tc=0.4 K;   750 mJ/molK2 CeMIn5 M=Co, Ir, Rh out of plane in-plane

  27. Angle integrated photoemission Experimental resolution ~30meV, theory predicts 3meV broad band Surface sensitive at 122eV ARPES Fujimori, 2006

  28. Buildup of coherence in single impurity case Very slow crossover! coherent spectral weight TK T Slow crossover more consistent with NP&F coherent spectral weight T T* T* NP&F: Nakatsuji,Pines&Fisk, 2004 Buildup of coherence coherence peak scattering rate Crossover around 50K

  29. Optical conductivity in LDA+DMFT • At 300K very broad Drude peak (e-e scattering, spd lifetime~0.1eV) • At 10K: • very narrow Drude peak • First MI peak at 0.03eV~250cm-1 • Second MI peak at 0.07eV~600cm-1

  30. 10K In eV Ce In Multiple hybridization gaps non-f spectra 300K • Larger gap due to hybridization with out of plane In • Smaller gap due to hybridization with in-plane In

  31. Summary part 4 • 115’s model systems to study the evolution of the f electron as a function of temperature • Multiple hybridization gaps in optics. • Very different Ce-In hybridizations with In out of plane being larger. J. Shim K Haule and G.K. Submitted to Science. (2007).

  32. PRL 80, (1998) GPalsson and GK Thermoelectricity near a Mott transition La1-xSrxTiO3

  33. Angle integrated photoemission vs DMFT Experimental resolution ~30meV, theory predicts 3meV broad band Surface sensitive at 122eV ARPES Fujimori, 2006

  34. Angle integrated photoemission vs DMFT • Nice agreement for the • Hubbard band position • SO split qp peak • Hard to see narrow resonance • in ARPES since very little weight • of q.p. is below Ef Lower Hubbard band ARPES Fujimori, 2006

  35. . arXiv:0704.1065 [pdf] • Title: Precise Control of Band Filling in NaxCoO2 • Authors: Daisuke Yoshizumi, Yuji Muraoka, Yoshihiko Okamoto, Yoko Kiuchi, Jun-Ichi Yamaura, Masahito Mochizuki, Masao Ogata, Zenji Hiroi • Comments: 4 pages, 5 figures, submitted to J. Phys. Soc. Jpn • Journal-ref: J. Phys. Soc. Jpn. 76 (2007) 063705 • Subjects: Strongly Correlated Electrons (cond-mat.str-el)

  36. DMFT Impurity cavity construction

  37. Functional formulation. Chitra and Kotliar Phys. Rev. B 62, 12715 (2000)and Phys. Rev.B (2001).  Introduce Notion of Local Greens functions, Wloc, Gloc G=Gloc+Gnonloc . Ex. Ir>=|R, r> Gloc=G(R r, R r’) dR,R’’ Sum of 2PI graphs One can also view as an approximation to an exact Spetral Density Functional of Gloc and Wloc.

  38. EDMFT loop G. Kotliar and S. Savrasov in New Theoretical Approaches to Strongly Correlated G Systems, A. M. Tsvelik Ed. 2001 Kluwer Academic Publishers. 259-301 . cond-mat/0208241 S. Y. Savrasov, G. Kotliar, Phys. Rev. B 69, 245101 (2004) • Full implementation in the context of a a one orbital model. P Sun and G. KotliarPhys. Rev. B 66, 85120 (2002). • After finishing the loop treat the graphs involving Gnonloc Wnonloc in perturbation theory. P.Sun and GK PRL (2004). Related work, Biermann Aersetiwan and Georges PRL 90,086402 (2003) .

  39. Anomalous Resistivity Maximum metallic resistivity

  40. Total Energy as a function of volume for Pu W(ev) vs (a.u. 27.2 ev) Pu Zein (2005) Following Aryasetiwan Imada Georges Kotliar Bierman and Lichtenstein. PRB 70 195104. (2004) (Savrasov, Kotliar, Abrahams, Nature ( 2001) Non magnetic correlated state of fcc Pu.

  41. Gouder Havela Lande PRB(2001)r alpa->delta Photoemission

  42. Photoemission Spectra[ Shim. Haule,GK Nature (2007)] alpa->delta volume collapse transition F0=4.5,F2=7.15 20 F0=4,F2=6.1

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