Collective excitations in the fractional quantum Hall effect of a multicomponent fermion system

We derive the dispersion of the elementary excitations in a two-component integer and fractional quantum Hall effect. We consider the fully polarized ground state and show the existence of both a magnetoroton mode and a low-lying Goldstone mode (GM). For the unpolarized ground state we derive the dispersion for both a density-density mode and a spin-wave mode both going to a finite value at small momentum q. We examine the extension of the charge-density-wave (CDW)-like ground state and fluidlike Laughlin state to multicomponents. We show that the latter has the lowest ground-state energy with a polarized ground state at filling factor {ν}=1, (1/3), and (1/5) and unpolarized at {ν}=(2/5). Most important, the CDW predicts a polarized ground state at {ν}=(2/5) and would, therefore, show dissipation via the GM channel contrary to the Laughlin-like ground states. We have, therefore, a new experimental possibility for selecting the correct ground state from many of the recent interesting suggestions.