Dielectric response of cylindrical nanostructures in a magnetic field

Abstract

We study the magnetic field dependence of the dielectric response of large cylindrical molecules such as nanotubes. When a field-induced level crossing takes place, an applied electric field causes a linear instead of the usual quadratic Stark effect. This results in a large dielectric response. Explicit calculations are performed for doped nanotubes and a rich structure in the real part of the low-frequency dielectric function ǫ ′ (H) is found when a magnetic field is applied along the cylinder axis. It is suggested that studies of ǫ ′ (H, T ) can serve as a spectroscopic tool for the investigation of large ringshaped or cylindrical molecules. PACS

Interaction effects on persistent current of ballistic cylindrical nanostructures

“…Thereby, any response function, providing that the electronic structure of the cylinder is preserved, are expected to show an abrupt change at the position of these crossing points where the total spin is changed. This should be the case in measures of persistent current [4], but also, in the static electric magnetopolarisability studied in [16] and already measured for an ensemble of metallic rings [25] and, as a last example, in magnetoconductance measurements, with bad contacts to the electrodes, such as the one done in [26] where multiwall carbon nanotubes behave as quantum dots. Similar effects were studied in [24] for quantum dots, where the spin transitions were shown to give characteristic signatures in the Coulomb-blockade peak positions.…”

“…Indeed, only the off-diagonal blocks are determined by using Eqs. (16) and (18). Additional assumptions are needed to fix the three diagonal blocks: here, we calculate these blocks as matrix elements of the one-particle operatorF ce , procedure particularly appropriate for closed shell configurations [21].…”

“…Note that the spectrum, and therefore every thermodynamic quantity, is periodic in flux, with periodicity φ = 1 [3]. As the magnetic field is increased, the energy levels evolve and many level crossings appear [16] (Cf. Fig.…”

“…For cylinders, in the pure case and without electron-electron interaction, an axial magnetic field induces many level crossings at different values of the magnetic flux [16]. At zero temperature, for a certain density of particles, the ground state energy shows also crossing points for particular values of the field where the ground state is degenerate.…”

Magnetopolarizability of mesoscopic systems

“…We attribute this effect to selection rules inherent to the square lattice which are responsible for the cancellation of the matrix elements of operator X between eigenstates close to a level crossing. In particular it has been shown [13] that these selection rules do not exist in the hexagonal lattice where giant magnetopolarisability is expected for particular values of flux at the same level of approximation.…”