Metal-insulator transitions

Transcription

1 Metal-insulator transitions Bandwidth control versus fillig control Strongly correlated Fermi liquids Spectral weight transfer and mass renormalization Bandwidth control Filling control Chemical potential shift

2 Metal-insulator transitions Bandwidth control versus fillig control.

3 Metal-insulator transition through collapse of Mott-Hubbard gap U > W U < W

4 Metal-insulator transition through hole doping into Mott-Hubbard insulator n = 1 n < 1

5 Bandwidth- versus filling-controlled metal-insulator transition U/W or /W BANDWIDTH Filling-controlled MIT 1 Bandwidth-controlled MIT n

6 Bandwidth- versus filling-controlled in Mott-Hubbard systems Bandwidth control Filling control

7 Metal-insulator transitions Strongly correlated Fermi liquids

8 Bandwidth- versus filling-controlled in Mott-Hubbard systems Bandwidth control Strongly correlated metal (Fermi liquid) Filling control

9 Spectral function of correlated Fermi liquid quasi-particle (QP) peak incoherent part incoherent part k F k F Fermi surface k F is defined by * Discontinuity in n k * E F crossing of infinitely sharp QP peak A. Damascelli et al., RMP 01

10 m*/m b ~ W b /W coh ~ v F,b /v F > 1: mass renormalization bandwidth Fermi velocity (m b : band mass, ) Correlation effects on spectral function A(k, (k,ω), band dispersion ε k, DOS ρ(ω), momentum distribution n(k) without electron correlation with electron correlation A(k,ω) non-interacting band A(k,ω) non-interacting band v F,b incoherent part W b coherent part W coh v F incoherent part

11 Spectral function A(k, (k,ω) without electron correlation Green s function spectral function DOS A(k,ω) = N b (ω) : band DOS band dispersion QP weight = 1

12 Effects of self-energy energy Σ (k,ω) on the spectral function A(k, (k,ω) Green s function ~ coherent part spectral function A(k,ω) ~ incoherent part band (QP) dispersion QP weight (renormalization factor) Im Re

13 Measuring A(k,ω) using angle-resolved photoemission spectroscopy (ARPES) EDC

14 Fermi-liquid behavior in ARPES spectra of 2D system TiTe 2 Self-energy near µ k k theoretical fit R. Claessen et al., PRL 92

15 Metal-insulator transitions Spectral weight transfer and mass renormalization Bandwidth control

16 Bandwidth-controlled metal-insulator transition in Mott-Hubbard systems θ W cos 2 θ Bandwidth control Hubbard picture? Brikman-Rice picture m* Filling control

17 Bandwidth-controlled metal-insulator transition in Mott-Hubbard systems Photoemission expt. on d 1 systems Hubbard model calc coherent part (quasi-particle bands) U / W <<1 m* ~ m b ~ W b U / W >1 W W coh U m* incoherent O 2p V 3d Incoherent part (Hubbard bands) A. Fujimori et al., PRL 92 X.Y. Zhang et al., PRL 93

18 Bandwidth-controlled d 1 Mott-Hubbard system Sr 1-x Ca x VO 3 Band calc. d 1 d 0 W b d 1 d 0 d 1 d 0 W coh Incoherent part (Hubbard bands) + surface coherent part (quasi-particle bands) m*/m b ~ W b /W coh ~ 1.7 K. Morikawa et al., PRB 95 H.I. Inoue et al., PRL 95

19 Bandwidth-controlled d 1 Mott-Hubbard system Sr 1-x Ca x VO 3 - surface or bulk? Electronic specific heat & Pauli-paramagnetic susceptibility Bulk-sensitive photoemission LDA m*/m b ~ 1.8 W b W coh CaVO 3 SrVO 3 H.I. Inoue et al., PRB 98 Incoherent part coherent part m*/m b ~ W b /W coh ~ 1.7 A. Sekiyama et al., PRL 04 cf) R. Eguchi et al., cond-mat/05

20 Band structure and Fermi surfaces of Sr 1-x Ca x VO 3 Band-structure calculation d xy d zx d yz X Γ Γ ε xy ε yz ε zx ( k) = ed + t0 (cos kxa + cos k ya) +... ( k) = ed + t0 (cos k ya + cos kza) +... ( k) = e + t (cos k a + cos k a)... d Γ R M 0 z x + Three 2D bands, Three cylindrical Fermi surfaces Fermi surface of CaVO 3 studied by de Haas-van Alphen measurements K. Takegahara et al., JES 94 H.I. Inoue et al., PRL 02

21 m*/m b ~ W b /W coh ~ v F,b /v F > 1: mass renormalization bandwidth Fermi velocity (m b : band mass, ) Correlation effects on spectral function A(k, (k,ω), band dispersion ε k, DOS ρ(ω), momentum distribution n(k) without electron correlation with electron correlation A(k,ω) non-interacting band A(k,ω) non-interacting band v F,b incoherent part W b coherent part W coh v F incoherent part

22 Band dispersion and mass renormalization in SrVO 3 m*/m b ~ v F,b /v F ~ 1.7 Fermi velocity Electronic specific heat m*/m b ~ 1.8 π Γ ν ν Γ I.H. Inoue et al, PRB 98 π T. Yoshida et al., cond-mat/05, to PRL

23 ARPES form 2D materials Momentum parallel to surface k II

24 ARPES form 3D materials X M X M Γ(103) k z Γ(003) X X k z X M X M 96 e 88 ev 74 ev k ll Momentum parallel to surface k ll k ll hν = 60 ev 68 ev Momentum perpendicular to surface k z z

25 Metal-insulator transitions Spectral weight transfer and mass renormalization Filling control

26 Filling-controlled metal-insulator transition in Mott-Hubbard systems Bandwidth control ? Filling control

27 Filling-controlled Mott-Hubbard system La 1-x Sr x TiO 3 Electronic specific heat & Pauli-paramagnetic suseptibility Kadowaki-Woods relationship x =0.05 x =0.2 x =0.1 x =0 rigid band model Wilson ratio: χ/γ ~ 2 x =0.3 x n=1/r H ~1-x Y. Tokura et al. PRL SrTiO 3 d 0 x x 0 LaTiO 3 d 1 Mott insulator

28 Filling-controlled Mott-Hubbard system La 1-x Sr x TiO 3 Photoemission expt SrTiO 3 d 0 Hubbard model calc δ = x + y δ AFM AFI Incoherent (LHB) T. Yoshida et al., EPL 02 coherent 0 µ ~ LaTiO 3 Mott insulator LHB UHB U H. Kajueter et al, PRB 96

29 Perovskite-type type transition-metal oxdies Bandwidth control Ti Mn A 2 BO 4 Textbook Fermi liquid Giant High-Tc Mott transition thermoelectricity Giant superconductivity Magnetoresistance Co Cu Filling control M. Imada, A. Fujimori and Y. Tokura, Rev. Mod. Phys. 98

30 Colossal magneto-resistance in filling-controlled system La 1-x Sr x MnO 3 M. Urushibara et al., PRB 95 Y. Tokura et al., JPSJ 94

31 Filling-controlled system La 1-x Sr x MnO 3 with colossal magneto-resistance extremely weak coherent part polaron effect? T. Saitoh et al., PRB 95

32 Metal-insulator transitions Chemical potential shift

33 Chemical potential shift in Fermi liquid charge susceptibility : F s0 : Landau parameter for e-e repulsion : electronic specific heat coefficient : quasi-particle density = ρ(ω)/z A. Fujimori et al., JES 02

34 Deducing chemical potential shift from core-level shifts T [K] 100 antiferromagnetic insulator pseudo-gap metal 10 normal metal (Fermi liquid) Core-level XPS spectra Core-level shifts 0 superconductor spin glass? Hole / Cu atom A. Ino et al., PRL 97

35 Transition-metal core levels Ti 4+ Ti 3+ YTiO3 Mott insulator 0 Ti 4+ /Ti 3+ intensity ratio x CaTiO 3 d 0 K. Morikawa et al., PRB 96

36 Deducing chemical potential shift from core-level shifts Core-level shifts Madelung potential Chemical potential shift Qualitatively different from expt. A. Ino et al., PRL 97 A. Fujimori et al., JES 02 N. Harima et al., PRB 01

37 QP-QP repulsion F s o and mass enhancement m*/m b Unusual pinning of chemical potential

38 Chemical potential shift pinning due to incommensurate CDW/SDW ~ stripes

39 Microscopic phase separation as the origin of chemical potential pinning

40 Chemical potential shift in filling-controlled systems AF γ as δ 0 1/8 chemical potential pinning incommensurate CDW/SDW ~ stripes 1/3 no chemical potential pinning commensurate CDW/SDW A. Fujimori et al., JES 02

41 Chemical potential shift in hole-doped CMR Mn perovskites Chemical potential shift µ (ev) no stripes Pr 1-x Ca x MnO 3 La 1-x Sr x MnO 3 stripes Stripes/bi-stripes x = x, carrier concentration x = 0.67 stripes K. Ebata et al. J. Matsuno et al., EPL 02 S.Mori et al., Nature 98 Y. Tokura and Y. Tomioka