  We simulate the optical and electrical responses in gallium-doped graphene.
Using density functional theory with a local density approximation, we
simlutate the electronic band structure and show the effects of impurity doping
(0-3.91\%) in graphene on the electron density, refractive index, optical
conductivity, and extinction coefficient for each doping percentages. Here,
gallium atoms are placed randomly (using a 5-point average) throughout a
128-atom sheet of graphene. These calculations demonstrate the effects of hole
doping due to direct atomic substitution, where it is found that a disruption
in the electronic structure and electron density for small doping levels is due
to impurity scattering of the electrons. However, the system continues to
produce metallic or semi-metallic behavior with increasing doping levels. These
calculations are compared to a purely theoretical 100\% Ga sheet for comparison
of conductivity. Furthermore, we examine the change in the electronic band
structure, where the introduction of gallium electronic bands produces a shift
in the electron bands and dissolves the characteristic Dirac cone within
graphene, which leads to better electron mobility.
