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Electronic excitations of double-walled armchair carbon nanotubes

This study investigates the geometric configurations and magneto-electronic excitations of double-walled armchair carbon nanotubes. The band structures, density of states, and response functions are analyzed, along with the effects of intertube interactions and the magnetic flux. The study concludes with insights into the low-energy bands and plasmon excitations of double-walled nanotubes.

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Electronic excitations of double-walled armchair carbon nanotubes

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  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. Geometric configurations--- Single-wall carbon nanotube a1 a2 armchair (m,m) Rx=m a1+n a2Ry=p a1+q a2

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

  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 Vppσ=6.38 eV Vppπ=-2.66 eV (γ0)

  7. Band structures without intertube interaction: • symmetric about EF , and EF=0 • linear bands intersecting at EF=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 S5 system

  10. Magnetoelectronic properties J → J+ψ/ψ0 shift angular momentum

  11. Band structures linear band → parabolic band, form energy spacing. • induce energy gap • break state degenercy. (0.04 ψ0~ 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. 3. Magneto electronic excitations e - φc (J,kz+q;σ,ψ) • energy transfer • momentum transfer: Δkz=q e - φv (J,kz;σ,ψ)

  15. Response function response function inner: χ1 outer: χ2

  16. Band structures Response functions

  17. 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 !

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