  We investigate theoretically the nonequilibrium finite-frequency current
noise in a four-terminal quantum point contact of interacting helical edge
states at a finite bias voltage. Special focus is put on the effects of the
single-particle and two-particle scattering between the two helical edge states
on the fractional charge quasiparticle excitations shown in the nonequilibrium
current noise spectra. Via the Keldysh perturbative approach, we find that the
effects of the single-particle and the two-particle scattering processes on the
current noise depend sensitively on the Luttinger liquid parameter. Moreover,
the Fano factors for the auto- and cross correlations of the currents in the
terminals are distinct from the ones for tunneling between the chiral edge
states in the quantum Hall liquid. The current noise spectra in the
single-particle-scattering-dominated and the two-particle-scattering-dominated
regime are shown. Experimental implications of our results on the transport
through the helical edges in two-dimensional topological insulators are
discussed.
