  We study the finite-frequency inter-band transition peak in the optical
conductivity of a heavy fermion system close to a Kondo breakdown quantum
critical point, where the lattice Kondo temperature vanishes. As the system
approaches the phase transition from the heavy Fermi liquid side, we find a new
cross-over regime where the peak position is related to, but is not directly
proportional to, the lattice Kondo scale. In particular, the position of the
peak moves to lower energies, but remains finite at the critical point. On the
other hand, the peak value changes non-monotonically and eventually the peak
disappears at the quantum critical point, indicating the decoupling of the
narrow band of f-electrons from the conduction band. We argue that these are
unique signatures of a Kondo breakdown transition, and therefore can be useful
to distinguish it experimentally from a spin density wave instability.
