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. In the long-wavelength limit, the dispersion of the collective excitations provided by the density-density response of the single-component HL matches that of spin-density response of the two-component HL.