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Collaborators: G.Kotliar, Ji-Hoon Shim, S. Savrasov

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

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Collaborators: G.Kotliar, Ji-Hoon Shim, S. Savrasov

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  1. Electronic Structure of Strongly Correlated Electron Materials: A Dynamical Mean Field Perspective. Collaborators:G.Kotliar, Ji-Hoon Shim, S. Savrasov Kristjan Haule, Physics Department and Center for Materials Theory Rutgers University Rutgers University Miniworkshop on New States of Stable and Unstable Quantum Matter, Trst 2006

  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 • Antiferromagnetic transition in Curium • 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. Effective (DFT-like) single particle Spectrum consists of delta like peaks Spectral density usually contains renormalized quasiparticles and Hubbard bands DMFT + electronic structure method • Basic idea of DMFT: reduce the quantum many body problem to a one site • or a cluster of sites problem, in a medium of non interacting electrons obeying a • self-consistency condition. (A. Georges et al., RMP 68, 13 (1996)). • DMFT in the language of functionals: DMFT sums up all local diagrams in BK functional Basic idea of DMFT+electronic structure method (LDA or GW): For less correlated bands (s,p): use LDA or GW For correlated bands (f or d): with DMFT add all local diagrams

  6. f7 L=0,S=7/2 J=7/2 f5 L=5,S=5/2 J=5/2 f1 L=3,S=1/2 J=5/2 f6 L=3,S=3 J=0 How good is single site DMFT for f systems? f1 L=3,S=1/2 J=5/2 f6 L=3,S=3 J=0

  7. Cerium

  8. 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

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

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

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

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

  13. 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)

  14. Americium

  15. 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)

  16. 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)

  17. 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!

  18. Curie-Weiss Tc Trends in Actinides alpa->delta volume collapse transition F0=4,F2=6.1 F0=4.5,F2=7.15 Same transition in Am under pressure F0=4.5,F2=8.11 Curium has large magnetic moment and orders antif.

  19. 5f7/2 valence 5f5/2 4d5/2->5f7/2 4d3/2->5f5/2 Excitations from 4d core to 5f valence Core splitting~50eV 4d3/2 Energy loss [eV] core 4d5/2 EELS & XAS Electron energy loss spectroscopy (EELS) or X-ray absorption spectroscopy (XAS) Branching ration B=A5/2/(A5/2+A3/2) 2/3<l.s>=-5/2(14-nf)(B-B0) B0~3/5 Measures unoccupied valence 5f states Probes high energy Hubbard bands! gives constraint on nf for given nf, determines <l.s>

  20. LS versus jj coupling in Actinides • Occupations non-integer except Cm • Close to intermediate coupling • Delocalization in U & Pu-> towards LS • Am under pressure goes towards LS • Curium is localized, but close to LS! • m=7.9mB not m=4.2mB K.T.Moore, et.al.,PRB in press, 2006 G. Van der Laan, et.al, PRL 93,27401 (2004) J.G. Tobin, et.al, PRB 72, 85109 (2005) d a

  21. What is captured by single site DMFT? • Captures volume collapse transition (first order Mott-like transition) • Predicts well photoemission spectra, optics spectra, • total energy at the Mott boundary • Antiferromagnetic ordering of magnetic moments, • magnetism at finite temperature • Qualitative explanation of mysterious phenomena, such as • the anomalous raise in resistivity as one applies pressure in Am,..

  22. 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

  23. 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

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

  25. 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 (2001)

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

  27. ~1eV Bi2212 Optical weight, plasma frequency Weight bigger in SC, K decreases (non-BCS) Weight smaller in SC, K increases (BCS-like) F. Carbone et.al, cond-mat/0605209

  28. ~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

  29. 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)

  30. 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)

  31. 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)

  32. Optics mass and plasma frequency Extended Drude model • In sigle site DMFT plasma frequency vanishes as 1/Z (Drude shrinks as Kondo peak shrinks) at small doping • Plasma frequency vanishes because the active (coherent) part of the Fermi surface shrinks • In cluster-DMFT optics mass constant at low doping doping ~ 1/Jeff line: cluster DMFT (cond-mat 0601478), symbols: Bi2212, F. Carbone et.al, cond-mat/0605209

  33. 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 elemental actinides and lanthanides single site LDA+DMFT gives the zeroth order picture • 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

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

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

  36. 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

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