Plasmons in single- and double-component helical liquids: Application to two-dimensional topological insulators

The plasmon excitations in proposed single- and double-component helical liquid (HL) models are investigated within the random-phase approximation, by calculating the density-density, spin-density and spin-spin waves. The effect due to broken time-reversal symmetry on intraband-plasmon dispersion relation in the single-component HL system is analyzed and compared to those of well-known cases, such as conventional quasi-one-dimensional electron gases and armchair graphene nanoribbons. The equivalence between the density-density wave in the single-component HL to the coupled spin-density and density-density waves in the double-component HL is shown here and explained, in addition to the difference between intraband and interband-plasmon excitations in these two systems. Since the two-component HL can physically be thought of as a Kramers pair in two-dimensional topological insulators, our proposed single-component HL model with broken time-reversal symmetry, which is an artificial construct, can be viewed as an "effective" model in this sense and its prediction may be verified in realistic systems in future experiments.