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Collaborators: G.Kotliar, S. Savrasov, V. Oudovenko

Electronic Structure of Strongly Correlated Electron Materials: A Dynamical Mean Field Perspective. Collaborators: G.Kotliar, S. Savrasov, V. Oudovenko. Kristjan Haule, Physics Department and Center for Materials Theory Rutgers University Rutgers University. Overview.

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Collaborators: G.Kotliar, S. Savrasov, V. Oudovenko

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  1. Electronic Structure of Strongly Correlated Electron Materials: A Dynamical Mean Field Perspective. Collaborators:G.Kotliar, S. Savrasov, V. Oudovenko Kristjan Haule, Physics Department and Center for Materials Theory Rutgers University Rutgers University

  2. Overview • Application of DMFT to real materials (Spectral density functional approach). Examples: • alpha to gamma transition in Ce, optics near the temperature driven Mott transition. • Mott transition in Americium under pressure • Extensions of DMFT to clusters. Examples: • Superconducting state in t-J the model • Optical conductivity of the t-J model

  3. Universality of the Mott transition Crossover: bad insulator to bad metal Critical point First order MIT Ni2-xSex V2O3 k organics 1B HB model (DMFT):

  4. Coherence incoherence crossover in the 1B HB model (DMFT) Phase diagram of the HM with partial frustration at half-filling M. Rozenberg et.al., Phys. Rev. Lett. 75, 105 (1995).

  5. mapping fermionic bath Dynamical Mean Field Theory Basic idea of DMFT: reduce the quantum many body problem to a one site or a cluster of sites, in a medium of non interacting electrons obeying a self consistency condition. Basic idea of Spectral density functional approach: instead of using functionals of the density, use more sensitive functionals of the one electron spectral function. [density of states for adding or removing particles in a solid, measured in photoemission]

  6. mapping fermionic bath DFT & DMFT from the unifying point of view Density functional theory observable of interest is the electron density Dynamical mean field theory: observable of interest is the local Green's function (on the lattice uniquely defined) DMFT approximation exact BK functional

  7. Spectral density functional theory G. Kotliar et.al., cond-mat/0511085 observable of interestis the "local“Green's functions (spectral function) Currently feasible approximations: LDA+DMFT and GW+DMFT: basic idea: sum-up all local diagrams for electrons in correlated orbitals LDA+U corresponds to LDA+DMFT when impurity is solved in the Hartree Fock approximation

  8. Periodic table f1 L=3,S=1/2 J=5/2 f6 L=3,S=3 J=0

  9. Cerium

  10. Ce overview  isostructural phase transition ends in a critical point at (T=600K, P=2GPa)  (fcc) phase [ magnetic moment (Curie-Wiess law), large volume, stable high-T, low-p]   (fcc) phase [ loss of magnetic moment (Pauli-para), smaller volume, stable low-T, high-p] with large volume collapse v/v  15 • Transition is 1.order • ends with CP

  11. LDA and LDA+U ferromagnetic f DOS total DOS

  12. LDA+DMFT alpha DOS TK(exp)=1000-2000K

  13. LDA+DMFT gamma DOS TK(exp)=60-80K

  14. Photoemission&experiment • A. Mc Mahan K Held and R. Scalettar (2002) • K. Haule V. Udovenko and GK. (2003) Kondo volume colapse (J.W. Allen, R.M. Martin, 1982) Fenomenological Landau approach:

  15. Optical conductivity + * * J.W. van der Eb, A.B. Ku’zmenko, and D. van der Marel, Phys. Rev. Lett. 86, 3407 (2001) + K. Haule, et.al., Phys. Rev. Lett. 94, 036401 (2005)

  16. Americium

  17. Americium f6 -> L=3, S=3, J=0 Mott Transition? "soft" phase f localized "hard" phase f bonding A.Lindbaum, S. Heathman, K. Litfin, and Y. Méresse, Phys. Rev. B 63, 214101 (2001) J.-C. Griveau, J. Rebizant, G. H. Lander, andG.KotliarPhys. Rev. Lett. 94, 097002 (2005)

  18. Am within LDA+DMFT Large multiple effects: F(0)=4.5 eV F(2)=8.0 eV F(4)=5.4 eV F(6)=4.0 eV S. Y. Savrasov, K. Haule, and G. KotliarPhys. Rev. Lett. 96, 036404 (2006)

  19. Am within LDA+DMFT from J=0 to J=7/2 Comparisson with experiment V=V0 Am I V=0.76V0 Am III V=0.63V0 Am IV nf=6.2 nf=6 Exp: J. R. Naegele, L. Manes, J. C. Spirlet, and W. MüllerPhys. Rev. Lett. 52, 1834-1837 (1984) • “Soft” phase very different from g Ce • not in local moment regime since J=0 (no entropy) Theory: S. Y. Savrasov, K. Haule, and G. KotliarPhys. Rev. Lett. 96, 036404 (2006) • "Hard" phase similar toaCe, • Kondo physics due to hybridization, however, • nf still far from Kondo regime Different from Sm!

  20. Beyond single site DMFT What is missing in DMFT? • Momentum dependence of the self-energy m*/m=1/Z • Various orders: d-waveSC,… • Variation of Z, m*,t on the Fermi surface • Non trivial insulator (frustrated magnets) • Non-local interactions (spin-spin, long range Columb,correlated hopping..) • Present in cluster DMFT: • Quantum time fluctuations • Spatially short range quantum fluctuations • Present in DMFT: • Quantum time fluctuations

  21. cluster in real space cluster in k space The simplest model of high Tc’s t-J, PW Anderson Hubbard-Stratonovich ->(to keep some out-of-cluster quantum fluctuations) BK Functional, Exact

  22. t’=0 What can we learn from “small” Cluster-DMFT? Phase diagram

  23. Insights into superconducting state (BCS/non-BCS)? BCS: upon pairing potential energy of electrons decreases, kinetic energyincreases (cooper pairs propagate slower) Condensation energy is the difference non-BCS: kinetic energydecreases upon pairing (holes propagate easier in superconductor) J. E. Hirsch, Science, 295, 5563 (2226)

  24. Optical conductivity optimally doped overdoped cond-mat/0601478 D van der Marel, Nature 425, 271-274 (2003)

  25. ~1eV Bi2212 Optical weight, plasma frequency Weight bigger in SC, K decreases (non-BCS) Weight smaller in SC, K increases (BCS-like) D. van der Marel et.al., in preparation

  26. ~1eV Experiments interband transitions intraband Hubbard versus t-J model • Kinetic energy in Hubbard model: • Moving of holes • Excitations between Hubbard bands Hubbard model U Drude t2/U Excitations into upper Hubbard band • Kinetic energy in t-J model • Only moving of holes Drude t-J model J no-U

  27. Kinetic energy change Kinetic energy increases cluster-DMFT, cond-mat/0601478 Kinetic energy decreases Kinetic energy increases cond-mat/0503073 Exchange energy decreases and gives largest contribution to condensation energy Phys Rev. B 72, 092504 (2005)

  28. J J J J Kinetic energy upon condensation underdoped overdoped electrons gain energy due to exchange energy holes gain kinetic energy (move faster) electrons gain energy due to exchange energy hole loose kinetic energy (move slower) BCS like same as RVB (see P.W. Anderson Physica C, 341, 9 (2000), or slave boson mean field (P. Lee, Physica C, 317, 194 (1999)

  29. Optics mass and plasma frequency Extended Drude model • Within DMFT, optics mass is m*/m=1/Z and diverges at the Mott transition • Plasma frequency vanishes as 1/Z (Drude shrinks as Kondo peak shrinks) • In cluster-DMFT optics mass constant at low doping doping • Plasma frequency vanishes because the active (coherent) part of the Fermi surface shrinks line: cluster DMFT (cond-mat 0601478), symbols: Bi2212, Van der Marel (in preparation)

  30. Optimal doping: Powerlaws cond-mat/0605149 D. van der Marel et. al., Nature 425, 271 (2003).

  31. Optimal doping: Coherence scale seems to vanish underdoped scattering at Tc optimally overdoped Tc

  32. Local density of states of SC Cluster DMFT STM study 1 Larger doping 6 Smaller doping • V shaped gap (d-wave) • size of gap decreases with doping • CDMFT-optimall doping PH symmetric

  33. 41meV resonance • Resonance at 0.16t~48meV • Most pronounced at optimal doping • Second peak shifts with doping (at 0.38~120meV opt.d.) and changes below Tc – contribution to condensation energy local susceptibility YBa2Cu3O6.6 (Tc=62.7K) Pengcheng et.al., Science 284, (1999)

  34. N=4,S=0,K=0 N=4,S=1,K=(p,p) N=3,S=1/2,K=(p,0) N=2,S=0,K=0 A(w) S’’(w) Pseudoparticle insight PH symmetry, Large t

  35. Conclusions • LDA+DMFT can describe interplay of lattice and electronic structure near Mott transition. Gives physical connection between spectra, lattice structure, optics,.... • Allows to study the Mott transition in open and closed shell cases. • In both Ce and Am single site LDA+DMFT gives the zeroth order picture • Am: Rich physics, mixed valence under pressure. • 2D models of high-Tc require cluster of sites. Some aspects of optimally doped, overdoped and slightly underdoped regime can be described with cluster DMFT on plaquette: • Evolution from kinetic energy saving to BCS kinetic energy cost mechanism • Optical mass approaches a constant at the Mott transition and plasma frequency vanishes • At optimal doping: Physical observables like optical conductivity and spin susceptibility show powerlaw behavior at intermediate frequencies, very large scattering rate – vanishing of coherence scale, PH symmetry is dynamically restored, 41meV resonance appears in spin response

  36. * LDA local in localized LMTO base DMFT SCC * Impurity solver Impurity problem (14x14): LDA+DMFT implementation

  37. Comparison of spectral weight cluster DMFT / Bi2212 Spectral weight (kinetic energy) changes faster with T in overdoped system – larger coherence scale Carbone et.al., in preparation

  38. Partial DOS 4f Z=0.33 5d 6s

  39. More complicated f systems • Hunds coupling is important when more than one electron in the correlated (f) orbital • Spin orbit coupling is very small in Ce, while it become important in heavier elements The complicated atom embedded into fermionic bath (with crystal fileds) is a serious chalange so solve! Coulomb interaction is diagonal in the base of total LSJ -> LS base while the SO coupling is diagonal in the j-base -> jj base Eigenbase of the atom depends on the strength of the Hund's couling and strength of the spin-orbit interaction

  40. Classical theories Mott transition (B. Johansson, 1974): Hubbard model f electrons insulating changes and causes Mott tr. spd electrons pure spectators Anderson (impurity) model Kondo volume colapse (J.W. Allen, R.M. Martin, 1982): hybridization with spd electrons is crucial (Lavagna, Lacroix and Cyrot, 1982) changes → chnange of TK bath f electrons in local moment regime either constant or taken from LDA and rescaled Fenomenological Landau approach:

  41. ab initio calculation LDA+DMFT is self-consistently determined bath for AIM contains tff and Vfd hopping • Kondo volume colapse model resembles DMFT picture: • Solution of the Anderson impurity model→ Kondo physics • Difference: with DMFT the lattice problem is solved (and therefore Δ must self-consistently determined)while in KVC Δ is calculated for a fictious impurity (and needs to be rescaled to fit exp.) • In KVC scheme there is no feedback on spd bans, hence optics is not much affected.

  42. An example Atomic physics of selected Actinides

  43. optics mass and plasma w Basov, cond-mat/0509307

  44. Two Site CDMFTin the 1D Hubbard model M.Capone M.Civelli V. Kancharla C.Castellani and Kotliar, PRB 69,195105 (2004)

  45. Luttinger Ward functional NCA Slave particle diagrammatic impurity solvers every atomic state represented with a unique pseudoparticle atomic eigenbase - full (atomic) base , where general AIM: OCA TCA ( )

  46. three band Hubbard model, Bethe lattice, U=5D, T=0.0625D SUNCA vs QMC two band Hubbard model, Bethe lattice, U=4D three band Hubbard model, Bethe lattice, U=5D, T=0.0625D

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