  We investigate properties of the ground state of a light quark matter with
heavy quark impurities. This system exhibits the "QCD Kondo effect" where the
interaction strength between a light quark near the Fermi surface and a heavy
quark increases with decreasing energy of the light quark towards the Fermi
energy, and diverges at some scale near the Fermi energy, called the Kondo
scale. Around and below the Kondo scale, we must treat the dynamics
nonperturbatively. As a typical nonperturbative method to treat the strong
coupling regime, we adopt a mean-field approach where we introduce a
condensate, the Kondo condensate, representing a mixing between a light quark
and a heavy quark, and determine the ground state in the presence of the Kondo
condensate. We show that the ground state is a topologically non-trivial state
and the heavy quark spin forms the hedgehog configuration in the momentum
space. We can define the Berry phase for the ground-state wavefunction in the
momentum space which is associated with a monopole at the position of a heavy
quark. We also investigate fluctuations around the mean field in the
random-phase approximation, and show the existence of (exciton-like) collective
excitations made of a hole $h$ of a light quark and a heavy quark $Q$.
