  We study the Landau damping in Bose-Fermi superfluid mixture at finite
temperature. We find that at low temperature, the Landau damping rate will be
exponentially suppressed at both the BCS side and the BEC side of Fermi
superfluid. The momentum dependence of the damping rate is obtained, and it is
quite different from the BCS side to the BEC side. The relations between our
result and collective mode experiment in the recently realized Bose-Fermi
superfluid mixture are also discussed.
