  The Higgs amplitude mode in superconductors is the condensed matter analogy
of Higgs bosons in particle physics. We investigate the time evolution of Higgs
amplitude mode in massless Dirac systems, induced by a weak quench of an
attractive interaction. We find that the Higgs amplitude mode in the
half-filling honeycomb lattice has a logarithmic decaying behaviour,
qualitatively different from the $1/\sqrt{t}$ decay in the normal
superconductors. Our study is also extended to the doped cases in honeycomb
lattice. As for the 3D Dirac semimetal at half filling, we obtain an undamped
oscillation of the amplitude mode. Our finding is not only an important
supplement to the previous theoretical studies on normal fermion systems, but
also provide an experimental signature to characterize the superconductivity in
2D or 3D Dirac systems.
