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 wires with a dielectric constant $κ$ much larger than that of its environment $κe$⁠, such dispersion law crosses over to a dispersionless three-dimensional-like law when the plasmon wavelength becomes shorter than the length $(a/2)(κ/κe)ln(κ/2κe)$ 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.