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. 
O. Roslyak, Godfrey Gumbs and D. H. Huang
cond-mat.mtrl-sci cond-mat.mes-hall