Plasmons in semiconductor and topological insulator wires with large dielectric constant

The dispersion law of plasmons running along thin wires with radius $a$ is known to be practically linear. We show that in a wire with a dielectric constant $\kappa$ much larger than that of its environment ${\kappa }_e$, such dispersion law crosses over to a dispersionless three-dimensional-like law when the plasmon wavelength becomes shorter than the length $(a/2) \sqrt{(\kappa/\kappa_e)\ln(\kappa/2\kappa_e)}$ at which the electric field lines of a point charge exit from the wire to the environment. This happens both in trivial semiconductor wires and wires of three-dimensional topological insulators.