  We study the topological charge fluctuations of an SU(2) lattice gauge theory
containing both N_f=2 and 4 flavors of Wilson fermion, at low temperature with
non-zero chemical potential $\mu$. The topological susceptibility, chi_T, is
used to characterize differing physical regimes as mu is varied between the
onset of matter at mu_o and and color deconfinement at mu_d. Suppression of
instantons by matter via Debye screening is also investigated, revealing
effects not captured by perturbative predictions. In particular, the breaking
of scale invariance leads to the mean instanton size rho becoming mu-dependent
in the regime between onset and deconfinement, with a scaling rho~1/mu^2 over
the range mu_o<mu<mu_d, resulting in an enhancement of chi_T immediately above
onset.
