  We theoretically study the Coulomb drag resistivity and plasmon modes
behavior for a system composed of two parallel p-type doped GaS monolayers with
Mexican-hat valence energy band using the Boltzmann transport theory formalism.
We investigate the effect of temperature,$\ T$, carrier density,$\ p$, and
layer separation,$\ d$, on the plasmon modes and drag resistivity within the
energy-independent scattering time approximation. Our results show that the
density dependence of plasmon modes can be approximated by$\ p^{0.5}$. Also,
the calculations suggest a$\ d^{0.2}$ and a$\ d^{0.1}$ dependencies for the
acoustic and optical plasmon energies, respectively. Interestingly, we obtain
that the behavior of drag resistivity in the double-layer metal
monochalcogenides swings between the behavior of a double-quantum well system
with parabolic dispersion and that of a double-quantum wire structure with a
large carrier density of states. In particular, the transresistivity value
reduces exponentially with increasing the distance between layers. Furthermore,
the drag resistivity changes as$\ T^{2}/p^{4}$ ($\ T^{2.8}/p^{4.5}$) at low
(intermediate) temperatures. Finally, we compare the drag resistivity as a
function of temperature for GaS with other Mexican-hat materials including GaSe
and InSe and find that it adopts higher values when the metal monochalcogenide
has smaller Mexican-hat height.
