Collective excitations in a two-component one-dimensional massless Dirac plasma

We study spectra of long-wavelength plasma oscillations in a system of two-energy split one-dimensional (1D) massless Dirac fermion subbands coupled by spin-orbit interaction. Such a system may be formed by edge subbands in semiconducting transition-metal dichalcogenide monolayers. Intrasubband transitions of massless Dirac fermions give rise to optical and acoustic gapless branches of intrasubband 1D plasmons. We reveal that the optical branch is of quantum character with group velocity being inversely proportional to the square root of the Planck constant, whereas the acoustic branch is a classical one with group velocity proportional to the geometric mean of the edge subband velocities. Spin-orbit interaction, allowing intersubband transitions in the system, results in the emergence of two branches of intersubband 1D plasmons: upper and lower ones. The upper and lower branches are gapped at small wave vectors and evolve with positive and negative group velocities, respectively, from energy splitting of the edge subbands at the Fermi level. Both intersubband branches adjoin the intersubband single-particle excitation continuum from above, while in the case of the edge subbands with unequal velocities the lower one experiences Landau damping at small wave vectors. In addition, the lower branch, attaining zero frequency at a nonzero wave vector, alters its group velocity from a negative to positive one.