  We study theoretically the electrical transport of two-dimensional (2D)
massive Dirac fermions, which are described by the 2 by 2 massive Dirac
Hamiltonian, and with a gap at the charge neutrality point. Through analytical
diagrammatical calculations of electrical conductivity in the presence of long
range Coulomb scattering centers, we show that attendant with the variation of
the Berry phase from 0 to {\pi} as the Fermi energy moves away from the Dirac
point/band boundary, a continuous Anderson-localization (AL) to
weak-localization (WL), and further to weak anti-localization (WAL) transition
occurs, implying a change in the sign of the magnetoresistance. Such transition
indicates the presence of metal-insulator transition (MIT) in this 2D system,
in contrast to the classical scaling theory. The WL to WAL transition occurs at
a certain critical Berry phase despite the concentration of Coulomb impurities,
while the MIT critical point, which is the distinguishing doping level
separating the AL and WL phases, depends on the competition of conventional
conductivity and the negative maximally crossed diagram (MCD) corrections near
the bottom of conduction band.
