  We investigate the effects of a magnetic impurity in a multiband touching
fermion system, specifically, a triple-component semimetal with a flat band,
which can be realized in a family of transition metal silicides (CoSi family).
When the chemical potential coincides with the flat band, it is expected that
the impurity response of this system will be very different from that of an
ordinary Dirac or Weyl semimetal of which the density of states at the Fermi
level vanishes. We first determine the phase diagram within the mean-field
approximation. Then, we study the local moment regime by employing two
different methods. In the low temperature regime, the Kondo screening is
analyzed by the variational wavefunction approach and the impurity
contributions to the magnetic susceptibility and heat capacity are obtained,
while at higher temperature, we use the equation of motion approach to
calculate the occupation number of the impurity site and the impurity magnetic
susceptibility. The results are compared and contrasted with those in the usual
Fermi liquid and the Dirac/Weyl semimetals.
