One-dimensional systems. Spin-charge separation in insulators Tomonaga-Luttinger liquid behavior Stripes: one-dimensional metal?

Transcription

1 One-dimensional systems Spin-charge separation in insulators Tomonaga-Luttinger liquid behavior Stripes: one-dimensional metal?

2 One-dimensional systems Spin-charge separation in insulators

3 Spin-charge separation in photoemission spectra of 1D Mott insulator E, k Spinon excitation E s ~ v s k s v s /a J ~ 0.1 ev Holon excitation E h ~ v h k h v h /a t ~ 0.5 ev -k = k s + k h -E = E s + E h spinon holon C. Kim et al., PRL 96, PRB 97

4 Spin-charge separation in photoemission spectra of 1D Mott insulator t-j model no double occopancy add hole(s) Heisenberg model

5 Spin-charge separation in photoemission spectra of 1D Mott insulator holon dispersion spinon dispersion ~ non-interacting band photoelectron: E, k -k = k s + k h -E = E s + E h C. Kim et al., PRL 96, PRB 97

6 1D D Mott-Hubbard insulator NaV 2 O 5 V 3.5+ (d 0.5 ) Magnetic susceptibility VO 5 pyramid Bonner-Fischer type with J ~ 560 K charge ordering One d electron per rung ideal 1D Heisenberg chain (cf. CuGeO 3 ) M. Isobe and Y. Ueda, JPSJ 96

7 ARPES of 1D Mott-Hubbard insulator NaV 2 O 5 V 3d O 2p O 2p band is dispersive only along the b-axis K. Kobayashi et al., PRL 98, 99

8 ARPES of 1D Mott-Hubbard insulator NaV 2 O 5 K. Kobayashi et al., PRL 98, 99

9 ARPES of 1D charge-transfer insulator Sr 2 CuO 2 ARPES dispersion cf) 2D cuprate C. Kim et al., PRL 96, PRB 97

10 ARPES of 1D charge-transfer insulator halogen-bridged MX chain [Ni[ Ni(chnx) 2 Br]Br 2 Ni 3+ : [(t 2g ) 6 (e g ) 1 ] half filled (S=1/2) gigantic optical non-linearity --> opto-electric devices d x2-y2 d z2 S.I. Fujimori. et al., PRL 02

11 Comparison between [Ni(chnx) 2 Br]Br 2 and Sr 2 CuO 2 [Ni(chxn) 2 Br]Br 2 (J~0.36eV) Sr 2 CuO 3 (J=0.16eV, t=0.55ev) He II (hν=40.8ev) Ne I (hν=16.8ev) d-p chain model

12 p-d model calculations for [Ni(chnx) 2 Br]Br 2 and Sr 2 CuO 2 Exact diagonalization of p-d-p-d- cluster by K. Okada in S.I. Fujimori. et al., PRL 02

13 One-dimensional systems Tomonaga-Luttinger liquid behavior

14 Spin-charge separation in photoemission spectra of 1D Mott insulator E, k Spinon excitation E s ~ v s k s v s /a J ~ 0.1 ev Holon excitation E h ~ v h k h v h /a t ~ 0.5 ev -k = k s + k h -E = E s + E h spinon holon C. Kim et al., PRL 96, PRB 97

15 Spin-charge separation in 1D metal E Holon excitation: no gap in metal E h = v h k h v h /a t ~ 0.5 ev π/a 0 π/a Spinon excitation E s = v s k s v s /a J ~ 0.1 ev k charge velocity v C > spin velocity v S

16 Spin-charge separation in the spectral function of 1D Luttinger liquid spinon holon ARPES A spinon holon AIPES (DOS) ρ(ω) µ ρ(ω) ~ ω α charge velocity v C > spin velocity v S D. Orgard et al, PRL 01 J. Voit, PRB 93 µ ω

17 AIPES (DOS) of quasi-1d metals metal Insulator B. Dardel et al, PRL 91 Turned out to be a 3D metal in subsequent transport studies M. Nakamura et al., PRB 94

18 Qusai-1D conductor DCNQI 2 Cu showing MIT Electrical resisitivity Cu + : Cu 2+ = 2:1 R. Kato group at RIKEN

19 Photoemission and XAS spectra of DCNQI 2 Cu Cu 2p XPS c-axis N 1s XAS pπ Cu + : Cu 2+ = 2:1 I.H.Inoue et al., PRB 92 A. Sekiyama et al., PRB 97

20 Photoemission spectra of DCNQI 2 Cu near E F Line-shape analyses metal power law power law + Fermi edge insulator No Fermi edge at E F A. Sekiyama et al., PRB 95

21 1D-3D dimensional crossover F ~ nesting strength ~ Q fluctuation effects (CDW, SDW, ) interchain transfer integral

22 Spin-charge separation in the spectral function of 1D Luttinger liquid ARPES spinon holon A spinon holon µ D. Orgard et al, PRL 01 J. Voit, PRB 93 V. Meden, K. Schonhammer, PRL 95

23 AREPS spectra of quasi-1d metal Li 0.9 Mo 6 O 17 Comparison with theoretical line shapes expt. theory holon? spinon? No CDW J. D. Denlinger et al., PRL 99 Disagreement with K. Smith, PRL (??)

24 Quasi-1D chain in PrBa 2 Cu 3 O 7 and double-chain in PrBa 2 Cu 4 O 8

25 Quasi-1D chain in PrBa 2 Cu 3 O 7 and double-chain in PrBa 2 Cu 4 O 8 anisotropic metal 1D metal CDW gap from optical study plane Cu 2+ chain Cu 2.5+ Pr 3.5+ π/4 π/4 π/4 Zhang-Rice singlet band is quarter-filled: k F = π/4 T. Mizokawa et al., PRB 99, PRL 00, PRB 02

26 Tomonaga-Luttinger-liquid behavior of Zn-doped PrBa 2 Cu 4 O 8 AIPES (DOS) Fermi edge? 1D Fermi surface 1D Fermi surface T. Mizokawa et al.,prb 02

27 One-dimensional systems Stripes: one-dimensional metal?

28 Phase diagram of high-t c cuprates diagonal stripes = spin glass 4a A B dynamical vertical stripes C Fermi surface Fermi Surface D k y % k x k x SG 2 6 X. J. Zhou et al., Science 99

29 Observation of incommensurate neutron peaks - vertical and diagonal stripes in LSCO diagonal stripes static K. Yamada et al., PRB 97 S. Wakimoto et al., PRB 99, 00 M. Matsuda et al., PRB 00 vertical stripes dynamical Nd subst. static

30 Static (vertical) charge stripes in La Nd y Sr x CuO 4 (x ~ 0.125) La 2-x-y Nd Hall coefficient R H Electrical resistivity One-dimensional! Metalllic! T. Noda et al., Science 99

31 Chemical potential shift in the presence of charge stripes

32 Origin of charge segregation

33 1D D Fermi surface segments coexisting with 2D Fermi surface 1.0 a Nd-LSCO(Sr0.10) b Nd-LSCO(Sr0.15) k y (π) c d D Fermi surface segment LSCO(Sr0.15) k x (π) X.J. Zhou et al., PRL 01 2D Fermi surface Energy window at E F ~ 30 mev

34 Stripe: one dimensional metal? Simulation using 1D metal model Expt. Model for LSCO in stripe phase J.D. Lee, T. Mizokawa and A.F, J. Phys. Soc. Jpn 01

35 T. Mizokawa et al., PRB 99, PRL 00 T. Yoshida et al., unpublished Hartree-Fock calculations for the Hubbard model 1D Fermi surface 1D Fermi surface segment 2D Fermi surface

36 Hartree-Fock calculations for the Hubbard model Vertical stripes Diagonal stripes M. Ichikawa and K. Machida, JPSJ 1999

37 Nodal quasi-particle forming a Fermi arc in La 1.97 Sr 0.03 CuO 4 La 1.97 Sr 0.03 T. Yoshida et al., cond-mat/02