SWCNTs as Tomonaga-Luttinger liquids : Experiments Ferenc Simon Institut für Materialphysik, Universität Wien

2. SWCNTs as Tomonaga-Luttinger liquids : Experiments Ferenc Simon Institut für Materialphysik, Universität Wien

3. Outline • TLL: theory/experimental predictions • Established evidences for TLL in SWCNTs • Ongoing research

4. What is a TLL? 3D: Weak correlations even for strong interactions -Fermi gas: non-interacting electrons • Fermi (Landau) liquid: • Non-interacting quasiparticles (Fermions) • dressed by the interactions (effective mass, QP lifetime)

5. What is a TLL? • 1D: Strong correlations even for weak interactions • Peierls instability

6. What is a TLL? Interactions Electron-phonon:Peierls instability (charge gap) Superconductivity (spin gap) Electron-electron:Mott-Hubbard insulator (charge gap) Spin-density wave (spin gap) Luttinger liquid (gapless)

7. What is a TLL? TLL: 1D electron system without spin and charge gaps Tomonaga 1950, Luttinger JMP 1963, Haldane J. Phys. C 1981 J. Voit, Rep. Prog. Phys. 58, 977 (1995) • Collective excitations: ws=vs|q|, s=charge, spinsSpinons, Holons • power-law behaviour of correlations with interaction dependent exponents, Kr, Ks (0: exterme correlated, 1 non-correlated) • spin-charge separation

8. El. specific heat • Spin-susceptibility • El. Compressibility • Structure factor • DOS • NMR relaxation

9. Phase diagram TLL parameter: g (Kr) Experimental realizations: semiconductor quantum wires, FQHE edges states, long organic chain molecules, nanotubes, ...

10. SWNTs Band structure predicts three types: • semiconductor if (2n+m)/3 not integer • metal if n=m (armchair nanotubes) • small-gap semiconductor otherwise (curvature-induced gap) Correlations: TLL with g=0.28R. Egger, and A. Gogolin, Phys. Rev. Lett. 79, 5082, (1997).C. Kane, L. Balents, and M. P. A. Fischer, Phys. Rev. Lett. 79, 5086 (1997). Ballistic conductors:

11. Experiments • Tunneling spectroscopy • Photoemission spectroscopy • NMR experiments 2 Nature, 3 PRL 1 Nature, 1 PRL 0

12. Outline • TLL: theory/experimental predictions • Established evidences for TLL in SWCNTs • Ongoing research

13. Tunneling experiments Theoretical predictions: R. Egger, and A. Gogolin, Phys. Rev. Lett. 79, 5082, (1997). C. Kane, L. Balents, and M. P. A. Fischer, Phys. Rev. Lett. 79, 5086 (1997). 1.1 Tunneling to SWCNTs from normal contacts M. Bokrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L.Balents, and P. L. McEuen Nature 397, 598 (1999). 1.2 AFM manipulated mechanical SWCNT junctions. Z. Yao, H. W.C. Postma, L. Balents, and C. Dekker, Nature 402, 273 (1999). H. W.C. Postma, M. de Jonge, Z. Yao, and C. Dekker, Phys Rev B 62, 10653 (2000). 1.3 MWCNT junctions A. Bachtold, M. de Jonge, K. Grove-Rasmussen, P. L. McEuen, M. Buitelaar, and C Schönenberger Phys. Rev. Lett. 87, 166801 (2001). 1.4 Spacially resolved tunneling oscillations (STS) J. Lee, S. Eggert, H. Kim, S.-J. Kahng, H. Shinohara, and Y. Kuk, Phys. Rev. Lett. 93, 166403 (2004).

14. Tunneling • Tersoff-Hamann Modell: • I ~ U.rspitze(EF) .rprobe(r0,EF) • rprobe...... DOS • Valid for: • Tip: s-Orbital • U << Barriere B • B ~ (Fsample+Ftip)/2- e|U|/2 • I ~ e-2kz, k~(2meB/h2)1/2

15. Characterisation of SWCNT: STM/STS Local probe, time consuming

16. Theoretical predictions Suppressed tunneling conductance Small bias Large bias Universal scaling Geometry dependent exponent TLL parameter: g=0.28

17. -Samples selected with high contact resistance -With a single quantum dot bulk end

18. Transport through multiple quantum dots? Ruled out Universal scaling observed g=0.24

19. AFM manipulated junctions Z. Yao, H. W.C. Postma, L. Balents, and C. Dekker, Nature 402, 273 (1999).

20. AFM manipulated junctions

21. MWCNTs: Diffusive or Quasiballistic Inner shells: disorder

23. Photoemission spectroscopy • Photoelectric effect: EB= hn -F -Ekin • Monochromatic light source: • X-Ray Al-Ka (1486.6 eV) • He-gas discharge (21.21 eV) • High resolution SES 200: • DE set to 10 meV, T=35 K • UPS:matrix element weighted density of states of the valence band electrons • XPS (eg. C1s): bonding environment chemical composition sample stoichiometry

24. Effect of dimensionality: Photoemission semiconducting metallic H. Ishii et al, Nature, 426, 540 (2003)

25. semiconducting metallic Effect of dimensionality: Photoemission Metallic SWCNT in a bundle of SWCNTare Luttinger liquids T = 35K M1 S2 S1 a = 0.43, g=0.18 good agreement with theoretical predictions and transport measurements H. Ishii et al, Nature, 426, 540 (2003); H. Rauf et al, PRL 93, 096805 (2004)

26. e- e- Intercalation Alkali-metal intercalation Sapphire film vapor UHV doping getter in-situ doping: UHV evaporation (5x10-10 mbar) Na, K, Rb, Cs and Ba SAES getters

27. Doping dependence of photoemission: low doping M1 S2 S1 0.46 0 S1, S2, and M1 shift to higher binding energy with increasing K/C smaller shift for M1Near EF: power law scaling changes and a=0 above K/C=1/150 H. Rauf et al. PRL 93, 096805 (2004)

28. Doping dependence of the LL parameter a Power law scaling vs. intercalation:a=0.43-0.46, g=0.18 up to K/C=1/500, DES1=0.25 eVa=0.35-0.3, g=0.22 K/C=1/500-1/150, DES1=0.3 eVa=0, g=1 above K/C=1/150, DES1>0.35 eV H. Rauf et al. PRL 93, 096805 (2004)

29. Outline • TLL: theory/experimental predictions • Established evidences for TLL in SWCNTs • Ongoing research

30. DWCNT from 13C enriched C60 : 12C : 13C Simon et al. PRL submitted

31. DWCNT from 13C enriched C60

32. NMR on 13C enriched inner tubes P. Singer, H. Alloul Inner tubes: -different isotropic shift 110 ppm (125 ppm)  more sp3 character -60 ppm broad lines (30 ppm)  - different bonding angles

33. Relaxation I. Distribution of T1s Stretched exponential fitted

34. Relaxation II. 100-400 K d =0.65 nm (Raman: d =0.68 nm)

35. Relaxation III. <100 K No field dependence No change in NMR signal Downturn at 20 K  True electronic behavior

36. Presence of a pseudogap or TLL? One parameter fit, D= 20(2) K J. P. Lu, PRL 1995 J. W.Mintmire and C. T. White PRL 1998

37. Conclusions S- and MSWCNT are TLLs Transport PES Awaiting: NMR