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Cellular-DMFT approach to the electronic structure of correlated solids.

Application to the sp, 3d,4f and 5f electron systems. Collaborators, N.Zein K. Haule M. Capone M. Civelli O Parcollet, S.Y. Savrasov. Cellular-DMFT approach to the electronic structure of correlated solids. G.Kotliar Physics Department and Center for Materials Theory Rutgers University.

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Cellular-DMFT approach to the electronic structure of correlated solids.

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  1. Application to the sp, 3d,4f and 5f electron systems. Collaborators, N.Zein K. Haule M. Capone M. Civelli O Parcollet, S.Y. Savrasov Cellular-DMFT approach to the electronic structure of correlated solids. G.Kotliar Physics Department and Center for Materials Theory Rutgers University. and CPHT Ecole Polytechnique , France. Pascal Chair de la Fondation de l’Ecole Normale. Indo-US conference on Novel and Complex Materials Kolkata (Calcuta-Calcute) –India – 25 -29 October 2005

  2. Outline • Some introductory comments about Dynamical Mean Field Theory. • sp’s systems. The gap problem in semiconductors. • 3d’s Electrons. Superconductivity and the Mott transition. High Tc. • 5f’s Mott transition across the actinide series, Plutonium and Americium. • 4f’s The Kondo collapse in ga Cerium. • Outlook

  3. Concept of Many Body Electronic Structure, correlated materials. Effective (DFT-like) single particle spectrum always consists of delta like peaks Real excitation spectrum can be quite different

  4. DMFT Cavity Construction. A. Georges and G. Kotliar PRB 45, 6479 (1992).First happy marriage of atomic and band physics. Extremize a functional of the local spectra or the local self energy. Resum all the local graphs using a self consistent impurity model Reviews: A. Georges G. Kotliar W. Krauth and M. Rozenberg RMP68 , 13, 1996 Gabriel Kotliar and Dieter Vollhardt Physics Today 57,(2004)

  5. How good is in practice the local approximation ? Cellular DMFT [Kotliar et. al. PRL (2001) ] Test in 1d Hubbard model Capone Civelli Sarma Castellani and Kotliar PRB69,195105 (2004) ]

  6. DMFT describes Incoherent and Coherent regimes. M. Rozenberg et. al. Phys. Rev. Lett. 75, 105 (1995) \ T/W Phase diagram of a Hubbard model at int with partial frustration at integer filling. [no density changes!] Evolution of the Local Spectra as a function of U,and T.

  7. Two paths for ab-initio calculation of electronic structure of strongly correlated materials Crystal structure +Atomic positions Model Hamiltonian Correlation Functions Total Energies etc. DMFT ideas can be used in both cases.

  8. 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 Spectral Density Functional of Gloc and Wloc.

  9. Order in Perturbation Theory Order in PT n=1 n=2 Basis set size. l=1 r=1 DMFT l=2 r site CDMFT r=2 GW+ first vertex correction l=lmax GW Range of the clusters

  10. Conclusions sp systems. • Not well described by single site DMFT. But very well described by first principles cdmft with relatively small clusters. [2 or 3 coordination spheres] • Weakly correlated materials. Use cheap impurity solvers. • Fast, self consistent way of getting first principles electronic structure without LDA. Good trends for semiconducting gaps and band withds.

  11. Earlier approximations as limiting cases. • Spectral Density Functional • LDA+DMFT Savrasov Kotliar and Abrahams Nature 410,793 (2001). V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997)

  12. The 3d’s • A large number of 3d elements and oxides are well described by single site DMFT but some materials require 2 CDMFT [ Mott Peierls systems ] , or 4 site cuprate [high Tc superconductors]. • CDMFT conceptual tool for formulating a dynamical version of the RVB theory,which removes the conceptual problems of earlier versions and accounts naturally for a large body of experimental observations. [ M. Capone, M. Civelli O. Parcollet and G. Kotliar in preparation ] Civelli et. al. PRL (2005).

  13. Conclusions 5f systems at the Mott boundary. Pu and Am. • Single site DMFT describes well, and even predicted, the total energy of phases, the phonon spectra, the photoemission spectra, of Am and Pu. • Qualitative explanation of mysterious phenomena, such as the negative thermal expansion in delta Pu, the volume contraction in the delta-epsilon transition, the anomalous raise in resistivity as one applies pressure to Am metal, etc…..

  14. Conclusions 4f materials • Single site DMFT describes well the photoemission, total energy, and optical spectra of alpha and gamma cerium. • Analysis of the DMFT results favors (and provides a moder reformulation of) the volume collapse transition.

  15. Application to sp systems. Zein Savrasov and Kotliar (2005). What is the range of the self energy in real solids ? 2nd order PT impurity solver.

  16. Gaps of semiconductors

  17. Band Structure of Si from GW+DMFT Convergence of energy bands in Si using real space local self-energy method. Energy, eV Cutoff Radius R (after Zein, Savrasov, Kotliar, to appear in condmat 2005)

  18. Conclusions sp systems. • Not well described by single site DMFT. But very well described by first principles cdmft with relatively small clusters. [2 or 3 coordination spheres] • Weakly correlated materials. Use cheap impurity solvers. • Fast, self consistent way of getting first principles electronic structure without LDA. Good trends for semiconducting gaps and band wdiths.

  19. Applications to 3d systems,High Temperature Superconductors. P.W. Anderson, Baskaran Zou and Anderson : connection between Mottness and High Tc. RVB approach

  20. RVB phase diagram of the Cuprate Superconductors. Superexchange. G. Kotliar and J. Liu Phys.Rev. B 38,5412 (1988) • The approach to the Mott insulator renormalizes the kinetic energy Trvb increases. • The proximity to the Mott insulator reduces T goes to zero. • Superconducting dome. Pseudogap evolves continously into the superconducting state. Related approach using wave functions:T. M. Rice group. Zhang et. al. Supercond Scie Tech 1, 36 (1998), Gross Joynt and Rice (1986) M. Randeria N. Trivedi , A. Paramenkanti PRL 87, 217002 (2001)

  21. Competition of AF and SC U /t << 8 or SC AF AF SC AF+SC d d

  22. Gap and d-wave order parameter vs doping.

  23. Tunneling spectra . . Low energy inset around the Fermi level

  24. Follow the “normal state” with doping. Evolution of the spectral function at low frequency. If the k dependence of the self energy is weak, we expect to see contour lines corresponding to Ek = const and a height increasing as we approach the Fermi surface.

  25. : Spectral Function A(k,ω→0)= -1/π G(k, ω→0) vs k U=16 t hole doped K.M. Shen et.al. 2004 2X2 CDMFT

  26. Approaching the Mott transition: CDMFT Picture • Fermi Surface Breakup. Qualitative effect, momentum space differentiation. Formation of hot –cold regions is an unavoidable consequence of the approach to the Mott insulating state! • D wave gapping of the single particle spectra as the Mott transition is approached. • Similar scenario was encountered in previous study of the kappa organics. O Parcollet G. Biroli and G. Kotliar PRL, 92, 226402. (2004) .

  27. Large Doping

  28. Small Doping

  29. The 3d’s • A large number of 3d elements and oxides are well described by single site DMFT but some materials require 2 CDMFT [ Mott Peierls systems ] , or 4 site cuprate [cuprate superconductors]. • CDMFT conceptual tool for formulating a dynamical version of the RVB theory,which removes the conceptual problems of earlier versions and accounts naturally for a large body of experimental observations. [ M. Capone, M. Civelli O. Parcollet and G. Kotliar in preparation ] Civelli et. al. PRL (2005).

  30. 5f’s Mott Transition in the Actinide Series Johansen Phil Mag. 30, 469(1974) . Revisit with modern DMFT tools. Savrasov and Kotliar PRL 84,3760 (2000) ………. J. Lashley et.al.(2004)

  31. Pu phases: A. Lawson Los Alamos Science 26, (2000) • Non magnetic LDA underestimates the volume of fcc Pu by 30%, Negative shear modulus. Bouchet et.al.12, 1723 (2000) . • LSDA predicts d Pu to be magnetic with a large moment ( ~5 Bohr). Experimentally Pu is not magnetic. [Lashley et. al. cond-matt 0410634] • Treating f electrons as core overestimates the volume by 30 %

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

  33. Phonon freq (THz) vs q in delta Pu X. Dai et. al. Science vol 300, 953, 2003

  34. 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)

  35. Double well structure and d Pu Qualitative explanation of negative thermal expansion[Lawson, A. C., Roberts J. A., Martinez, B., and Richardson, J. W., Jr. Phil. Mag. B, 82, 1837,(2002). G. Kotliar J.Low Temp. Physvol.126, 1009 27. (2002)] F(T,V)=Fphonons+Finvar Natural consequence of the conclusions on the model Hamiltonian level. We had two solutions at the same U, one metallic and one insulating. Relaxing the volume expands the insulator and contract the metal.

  36. Approach the Mott point from the right Am under pressure Experimental Equation of State (after Heathman et.al, PRL 2000) Mott Transition? “Soft” “Hard” Density functional based electronic structure calculations: • Non magnetic LDA/GGA predicts volume 50% off. • Magnetic GGA corrects most of error in volume but gives m~6mB (Soderlind et.al., PRB 2000). • Experimentally, Am hasnon magnetic f6ground state with J=0(7F0)

  37. Am equation of state. LDA+DMFT.New acceleration technique for solving DMFT equations S. Savrasov K. Haule G. Kotliar cond-mat. 0507552 (2005)

  38. Resistivity of Am under pressure. J. C. Griveau Rebizant Lander and Kotliar PRL 94, 097002 (2005).

  39. Photoemission spectra using Hubbard I solver [Lichtenstein and Katsnelson, PRB 57, 6884,(1998 ), Svane cond-mat 0508311] and Sunca . [Savrasov Haule and Kotliar cond-mat 0507552] Hubbard bands width is determined by multiplet splittings.

  40. Photomission Spectra of Am under pressure. Sunca. Onset of mixed valence. Savrasov Haule Kotliar (2005)

  41. Conclusions 5f systems at the Mott boundary. Pu and Am. • Single site DMFT describes well, and even predicted, the total energy of phases, the phonon spectra, the photoemission spectra, of Am and Pu. • Qualitative explanation of mysterious phenomena, such as the negative thermal expansion in delta Pu, the volume contraction in the delta-epsilon transition, the anomalous raise in resistivity as one applies pressure to Am metal, etc…..

  42. Conclusion • CDMFT, method under very active development. But there is now a clear formulation (and to large extent implementation) as a fully self consistent, controlled many body approach to solids. • It gives good quantitative results for total energies, phonon and photoemission spectra, and transport of materials using elements from all over the periodic table. • Helpful in developing intuition and qualitative insights in correlated electron materials. • Review, G. Kotliar S. Savrasov K. Haule O. Parcollet V. Udovenko and C. Marianetti, submitted to RMP. Software , and modern programming tools for development and implementation of realistic DMFT http://dmftreview.rutgers.edu

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