Plasmons in semiconductor and topological insulator wires with large dielectric constant

TL;DR

This paper investigates how high dielectric constants in semiconductor and topological insulator wires alter the dispersion law of plasmons, revealing a transition from linear to dispersionless behavior at short wavelengths.

Contribution

It demonstrates that large dielectric constants cause a crossover in plasmon dispersion from linear to dispersionless in both semiconductor and topological insulator wires.

Findings

Dispersion law becomes dispersionless at short wavelengths for high dielectric constant wires.

The crossover wavelength depends on wire radius and dielectric constants.

Applicable to both trivial semiconductor and topological insulator wires.

Abstract

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.