Dielectric response of cylindrical nanostructures in a magnetic field

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 $\epsilon'(H)$ is found when a magnetic field is applied along the cylinder axis. It is suggested that studies of $\epsilon'(H, T)$ can serve as a spectroscopic tool for the investigation of large ring-shaped or cylindrical molecules.