  We establish the time decay rates of the solutions to the Cauchy problem for
the two-species Vlasov-Poisson-Boltzmann system near Maxwellians via a refined
pure energy method. The negative Sobolev norms are shown to be preserved along
time evolution and enhance the decay rates. The total density of two species of
particles decays at the optimal algebraic rate as the Boltzmann equation, but
the disparity between two species and the electric field decay at an
exponential rate. This phenomenon reveals the essential difference when
compared to the one-species Vlasov-Poisson-Boltzmann system in which the
electric field decays at the optimal algebraic rate or the Vlasov-Boltzmann
system in which the disparity between two species decays at the optimal
algebraic rate. Our proof is based on a family of scaled energy estimates with
minimum derivative counts and interpolations among them without linear decay
analysis, and a reformulation of the problem which well displays the
cancelation property of the two-species system.
