Electronic excitations of doublewalled armchair carbon nanotubes Geometric
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
Geometric configurations --- Single-wall carbon nanotube a 1 a 2 armchair (m, m) Rx=m a 1+n a 2 Ry=p a 1+q a 2
Geometric configurations--- Double-walled carbon nanotubes intertube distance: 3. 39 Å, closed to interlayer spacing of graphite.
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)
the tight-binding model
Intratube & intertube interactions Vppσ=6. 38 e. V Vppπ=-2. 66 e. V (γ 0)
Band structures without intertube interaction: • symmetric about EF , and EF=0 • linear bands intersecting at EF=0 , so metallic • parabolic band with double degenercy
Band structures with intertube interaction: • breaks symmetry of band structures • changes energy dispersion • localization of wavefunction: △: inner tube ○: outer tube
Density of states • linear bands →pleataues • parabolic bands →square-root divergences • several low-energy divergences in S 5 system
Magnetoelectronic properties J → J+ψ/ψ0 shift angular momentum
Band structures linear band → parabolic band, form energy spacing. • induce energy gap • break state degenercy. (0. 04 ψ0~ 114 Tesla)
Density of states • linear band to parabolic band → pleataue to divergence • break degenercy → more divergences
ψ-dependent energy gap • magnetic flux induces energy gap • intertube interactions & spin-B interactions reduces energy gap
3. Magneto electronic excitations ec - φ (J, kz+q; σ, ψ) • energy transfer • momentum transfer: Δkz=q eφv (J, kz; σ, ψ)
Response function response function inner: χ1 outer: χ2
Band structures Response functions
Response functions
Intertube Coulomb interactions: Random-Phase Approximation (RPA)
Loss function • Intertube interactions enrich electron-hole excitations, thus reduce plasmon intensity • Plasmons appears at certain q region
Loss function • Plasmon frequencies almost unchanged by the magnetic flux • Plasmon intensity reduced by the magnetic flux
q-dependent plasmon frequencies • more plasmon modes • acoustic plasmons to optical plasmons
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 electronenergy loss spectroscopy (EELS).
Thanks for your attention !
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