1. Electronic excitations of double-walled armchair carbon nanotubes Geometric configurations Magneto band structures Magneto electronic excitations Conclusions 何彥宏 ‚ 林明發 教授 ( 指導教授 ) 成功大學 物理系

2. R x =m a 1 +n a 2 R y =p a 1 +q a 2 Geometric configurations --- Single-wall carbon nanotube armchair (m,m) a1a1 a2a2

3. intertube distance: 3.39 Å, closed to interlayer spacing of graphite. Geometric configurations --- Double-walled carbon nanotubes

4. Double-walled armchair carbon nanotubes (5,5)-(10,10) 3 kinds of symmetric structures, due to translation and rotation symmetry 12 atoms in a primitive unit cell: (4 from inner tube) (8 from outer tube)

5. the tight-binding model

6. Intratube & intertube interactions V ppπ =-2.66 eV (γ 0 ) V ppσ =6.38 eV

7. Band structures without intertube interaction: symmetric about E F, and E F =0 linear bands intersecting at E F =0, so metallic parabolic band with double degenercy

8. Band structures with intertube interaction: breaks symmetry of band structures changes energy dispersion localization of wavefunction: △ : inner tube ○ : outer tube

9. Density of states linear bands →pleataues parabolic bands →square-root divergences several low-energy divergences in S 5 system

10. Magnetoelectronic properties J → J+ ψ / ψ 0 shift angular momentum

11. Band structures linear band → parabolic band, form energy spacing. induce energy gap break state degenercy. (0.04 ψ 0 ~ 114 Tesla)

12. Density of states linear band to parabolic band → pleataue to divergence break degenercy → more divergences

13. ψ -dependent energy gap magnetic flux induces energy gap intertube interactions & spin-B interactions reduces energy gap

14. e - φ c (J,k z +q;σ, ψ ) φ v (J,k z ;σ, ψ ) 3. Magneto electronic excitations energy transfer momentum transfer: Δk z =q

15. Response function response function inner: χ 1 outer: χ 2

16. Band structures Response functions

18. Intertube Coulomb interactions: Random-Phase Approximation (RPA)

19. Loss function Intertube interactions enrich electron-hole excitations, thus reduce plasmon intensity Plasmons appears at certain q region

20. Loss function Plasmon frequencies almost unchanged by the magnetic flux Plasmon intensity reduced by the magnetic flux

21. q-dependent plasmon frequencies more plasmon modes acoustic plasmons to optical plasmons

22. 4. Conclusion The intertube interactions alter the low energy bands, enrich the low-frequency single-particle excitations. The main features of the low-frequency plasmons are dominated by the momentum transfer q, the intertube interactions and the symmetric geometry. Double-walled geometry could be determined by the electron- energy loss spectroscopy (EELS).

23. Thanks for your attention !