Narrow Results

We discuss recent measurements of the interband spectrocopy of carbon nanotubes and studies of cyclotron resonance in graphene, using these to examine the possible dependence of the band structure of graphene on the number of layers present and the role of Coulomb interactions. Cyclotron resonances gives a value for the electron velocity at the Dirac point of 1.093×10⁶ ms^-1, which is ~ 20% larger than would be expected from deductions of the band structure of carbon nanotubes. In addition, a significant asymmetry exists between band structure for electrons and holes, which gives rise to a 5% difference between the velocities at energies of 125 meV away from the Dirac point.

The Fermi level for a multiwalled carbon nanotube is determined analytically by using the Fermi velocity obtained from the particle-in-a-box model. Fermi energy is found to be quantized so that the corresponding quantum number coincides with the wall number. In addition, the classical limit is discussed.

We study, by utilizing analytic techniques, electrical conduction in multiwalled carbon nanotubes. In fact, by using the well-known concept of Fermi velocity and the Drude theory, a mathematical relationship for conductance is derived so that this conductance is found to be quantized. In addition, our results are compared with experimental data.

The optical potential of an attractive nonrelativistic electron gas interacting with nuclear matter is determined on the basis of the concept of degenerate Fermi gas. In fact, the involved electrons are treated as three-dimensional quantum harmonic oscillators confined at the surface of a spherical (approximately ideal) potential well. Within this picture, the Fermi velocity is calculated as well as the spatial electron density at the surface of the potential well and the attractive force between the electron gas and the nuclear matter. In addition, considerations related to the Lippmann–Schwinger model are made.

For the first time, we present a theoretical formulation to determine the nonrelativistic repulsive optical potential relative to neutron–nucleus interaction in terms of the s-wave coherent scattering amplitude and the radius of the nucleus which is regarded as a spherical infinite potential well. Within this context, the Fermi velocity is determined in excellent agreement with the Fermi velocity obtained from considerations relative to nuclear density obeying the Saxon–Woods distribution. Assuming this distribution, the force relative to the neutron–nucleus interaction is calculated. Aspects related to the involved chemical potential are discussed. Our results are consistent with previous work.

By considering excitons in a semiconductor nonparabolic quantum dot as hydrogen-atom-like quasi-particles confined in a spherical quantum box, the dot being connected to two semi-infinite conducting leads, we propose a theoretical-analytical approach by which the maximal dot-lead coupling energy is calculated in terms of the maximum Fermi velocity. In addition, numerical computations consistent with the above approach are carried out. Our results constitute a deep insight into the state of the art and agree with experimental data.