Mott insulators. Mott-Hubbard type vs charge-transfer type
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1 Mott insulators Mott-Hubbard type vs charge-transfer type Cluster-model description Chemical trend Band theory Self-energy correction Electron-phonon interaction
2 Mott insulators Mott-Hubbard type vs charge-transfer type
3 Correlated electron systems/ Complex materials La 2-x Sr x CuO 4 Ga 1-x Mn x As
4 Lattice models for transition-metal compounds Hubbard model p-d model Transition metal ion (with d orbitals) Non-metal anion (with p orbitals)
5 Lattice models for transition-metal compounds (degenerate) Hubbard model p-d model t-j model no double occopancy
6 Band gap excitations - relevant to charge transport Hubbard model U p-d model U Charge transfer energy: on-site Coulomb energy: U
7 Photoemission spectroscopy
8 Mott-Hubbard Hubbard-type insulators vs charge-transfer transfer-type type insulators chemical potential µ W UHB UHB Inversephotoemission spectra W LHB Oxygen p band U < Oxygen p band LHB U > Photoemission spectra Mott-Hubbard gap Charge-transfer gap ~ U - W ~ -W UHB: upper Hubbard band LHB: lower Hubbard band Charge transfer energy: on-site Coulomb energy: U Band width: W
9 Mott insulators Cluster-model description
10 Cluster model for transition-metal oxides BO 6 cluster model AB 2 O 4 spinel ABO 3 perovskite perovskite are treated as adjustable parameters L: ligand (p) hole
11 Many-electron energy levels vs single-particle energy level Photoemission Inverse photoemission Ground state Inversephotoemission spectra E N+1 spectra E N-1 µ Photoemission E g µ : chemical potential E g : band gap
12 Mott-Hubbard type versus charge-transfer type many-electron energy level scheme Charge-transfer type insulator U > Mott-Hubbard type insulator U < N
13 Configuration-interaction interaction cluster-model analysis of d-electron photoemission satellites d n-1 final state U - d n L final state charge-transfer type U > -U Mott-Hubbard type U <
14 Configuration-interaction interaction cluster-model analysis vs LDA band theory for NiO LDA band calc. t 2g satellite O 2p e g t 2g e g O 2p G.A. Sawatzky and J.W. Allen, PRL 84 A. Fujimori and F. Minami, PRB 83 T. Oguchi et al., PRB 83
15 Chemical trend Mott insulators
16 Systematic variation of band gaps in transition-metal oxides U eff, eff T. Arima et al., PRB 93
17 Systematic variation of band gaps in transition-metal oxides U eff, eff : Eestimated from ionic model T. Arima et al., PRB 93
18 Systematic materials dependence of charge-transfer energy Z v ~ 23 ev, 22.5 ev for selenides, tellurides A.E. Bocquet et al., PRB 92
19 Systematic materials dependence of on-site Coulomb energy U Z v A.E. Bocquet et al., PRB 92
20 Systematic materials dependence of p-d transfer integral T pd 3(pdσ), 2(pdπ) A.E. Bocquet et al., PRB 92
21 Zaanen-Sawatzky Sawatzky-Allen diagram = W E g ~ W charge-transfer regime 3+ charge-transfer regime p-metal d-metal Mott-Hubbard regime E g ~ U - W U = W 4+ negative- regime Mott-Hubbard regime J. Zaanen, G.A. Sawatzky, J.W. Allen, PRL 85 A.E. Bocquet et al., PRB 96
22 Mott-Hubbard Hubbard-type insulators vs charge-transfer transfer-type type insulators chemical potential µ W UHB UHB Inversephotoemission spectra W LHB Oxygen p band U < Oxygen p band LHB U > Photoemission spectra Mott-Hubbard gap Charge-transfer gap ~ U - W ~ -W UHB: upper Hubbard band LHB: lower Hubbard band Charge transfer energy: on-site Coulomb energy: U Band width: W
23 Systematic variation of band gaps in transition-metal oxides U eff, eff U eff, eff : Eestimated from ionic model T. Arima et al., PRB 93
24 Multiplet corrections for Mott-Hubbard gap and charge-transfer gap Correction for charge-transfer energy: eff Multiplet corrections for and U Correction for on-site Coulomb energy: U U eff CT gap is reduced d 4 d 5 M-H and CT gap is enhanced T. Saitoh et al., PRB 95
25 Multiplet corrections for Mott-Hubbard gap and charge-transfer gap Optical gaps Calculated band gaps d 3 d 3 T. Arima et al., PRB 93 T. Saitoh et al., PRB 95
26 Band theory Mott insulators
27 Hartree-Fock and LDA+U band calculations - failure of LDA in NiO - Hartree-Fock band calc. t 2g e e g g t 2g O 2p E g ~ 4 ev Local-density-approximation (LDA) band calc.- NiO (14 valence electrons) t 2g (3) e g (2) O 2p(6) t 2g (3) e g (2) E g ~ 0.2 ev T. Mizokawa and A.F., PRB 96 e g LDA+U band calc. t 2g t 2g O 2p E g ~ 4 ev e g O 2p(6) t 2g (6) e g (4) CoO, FeO: metallic! V.I. Anisimov et al., PRB 91 T. Oguchi et al., PRB 83
28 Failure of LDA in Mott insulators Hartree-Fock potential energy (also for LDA+U) : occupation number of orbital i orbital-dependent self-consistent potential positive feedback toward orbital polarization Local-density approximation (LDA) potential energy : total occupation number (local density) spherically averaged potential, unphysical self-interaction orbital polarization suppressed
29 Orbital ordering in perovskite-type type ABO 3 compounds orbital 1 orbital 2 ex) LaMn 3+ O 3 Jahn-Teller distortion d 4 : t 2g 3 e g
30 Mott insulators Self-energy correction
31 Hartree-Fock band calculation + self-energy energy correction Σ(ω) Mott-Hubbard type Charge-transfer type O 2p band V 3d band V 3d O 2p expt expt Ni 3d O 2p Green s function: Spectral function: calculated with 2nd order perturbation Hartree-Fock eigenvalue T. Mizokawa and A. Fujimori, PRB 96
32 CI cluster model, Hartree-Fock band theory and photoemission spectra Experimental input band gaps magnetic moment hybridization strength
33 Mott insulators Electron-phonon interaction
34 Discrepancy of spectral line shapes between band theory and photoemission spectra DOS (states/ev f.u.) Mott-Hubbard type insulator VO 2 VO 2 /TiO 2 (001) O 2p band band calc. spectrum (280K) V 3d band Binding Energy (ev) Resistivity (ohm cm) insulating phase c PO 2 = 1 Pa T s = 583 K T s = 553 K TiO 2 (001) 250 T s = 643 K 300 metallic phase T MI bulk LDA+U band-structure calculation, X. Hunag, et al., cond-mat/98 Temperature (K) Y. Muraoka et al.
35 Electron-phonon interaction in the insulating phase of VO 2 Simulations using independent-boson model multiple-phonon lines zero-phonon line Energy /ω 0 K. Okazaki et al. PRB 04
36 Electron-phonon interaction in the insulating phase of VO 2 Simulations using independent-boson model multiple-phonon lines zero-phonon line Electron + lattice energy Zero-phonon line N-1-electron Frank-Condon transition N-electron Local co-ordinate Energy /ω 0
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