Why is CNT considered a 1D structure despite having movement in two dimensions?

  • Context: Graduate 
  • Thread starter Thread starter Halaaku
  • Start date Start date
  • Tags Tags
    1d Structure
Click For Summary
SUMMARY

Carbon Nanotubes (CNTs) are classified as one-dimensional (1D) structures due to their macroscopic length along the axis and atomic-scale circumference. The electronic behavior of CNTs is derived from the band structure of graphene, characterized by a linear dispersion relation: E = h_cut vF |k|, where k represents the 2D wavevector and vF is the Fermi velocity. Although CNTs exhibit movement in two dimensions due to quantized circumferential states, the electrons primarily move along the axial direction, leading to their classification as 1D structures. This unique behavior is influenced by temperature, which can affect energy levels but does not alter the fundamental 1D classification.

PREREQUISITES
  • Understanding of graphene band structure
  • Familiarity with the concept of Fermi velocity (vF)
  • Knowledge of wavevector (k) in two-dimensional systems
  • Basic principles of quantum mechanics related to electron movement
NEXT STEPS
  • Explore the electronic properties of graphene and their implications for CNTs
  • Study the effects of temperature on energy levels in CNTs
  • Investigate the quantization of circumferential states in nanostructures
  • Learn about the applications of CNTs in nanotechnology and materials science
USEFUL FOR

Researchers, materials scientists, and students in nanotechnology or condensed matter physics who are interested in the electronic properties and classifications of carbon nanotubes.

Halaaku
Messages
23
Reaction score
0
The electronic structure of CNT is discussed on the basis of band structure of
graphene. Graphene has a linear dispersion relation:
E = h_cut vF |k|
where k is the 2D wavevector and vF is the Fermi velocity. CNTs are
macroscopic along the axis but have a circumference of atomic dimensions, which
suggests that there will be large states in the axial direction but quantized
circumferential states. this implies that there are allowed transitions between circumferential states such that the movement is in the direction perpendicular to the axial direction of CNT. Therefore the movement is in two dimensions, yet we say CNT is a 1D structure. Why is that the case?
 
Physics news on Phys.org
The second dimension does not appear as "dimension" - the electrons do not move in that direction, even if it might give additional energy levels (depending on the temperature).
 

Similar threads

Graduate Problem about electronic structure
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Instability of a 1D material due to Fermi surface nesting
  • · Replies 8 ·
Replies
8
Views
3K
  • Poll Poll
Graduate Our picks for second quarter 2009 MIP (most important QG paper)
  • · Replies 13 ·
Replies
13
Views
5K
Mathematica This Week's Finds in Mathematical Physics (Week 262)
  • · Replies 4 ·
Replies
4
Views
3K
Graduate MOND Theory Primer: Stacy McGaugh's Research Program Explored
  • · Replies 11 ·
Replies
11
Views
4K
Textbooks on Condensed Matter Physics
  • · Replies 19 ·
Replies
19
Views
18K