  We study the effect of weak disorder on the delocalization properties of
gapped graphene superlattice (SL) formed by periodically located rectangular
potential barriers. We consider two types of the SLs: the SLs with uniform and
nonuniform gap. Using the perturbative approach we obtain an analytical
expression for the inverse localization length (ILL) derived for the case of
randomly fluctuating geometric and energetic parameters. In the first case,
when the barrier (well) width fluctuates around its mean value, the
corresponding equation for the ILL reveals the presence of the Fabry-Perot
resonances, at which the localization length diverges. These resonances are
exact, i.e., are stored in any degree of disorder. It has been found that the
localization properties manifest stronger for the particles with energies lying
in the non-resonant bands where our approach is extremely sensitive to the
degree of disorder. For the case of weakly fluctuating both barrier and well
widths we analytically obtain ILL taking correlations into account. The main
effect of the correlations, which lead to an increase (or decrease) in the
localization length, was revealed near the double resonance arising at
coincidence of two Fabry-Perot resonances associated with barrier and well
widths. The random fluctuations of the potential strength also lead to the
delocalization resonances. However, they exist only in a weak-disorder
approximation. We found that, for an array composed of alternating strips of
gapless and gapped graphene modifications these resonances can appear only for
normally incident particles in contrast to the SL with a uniform gap. For such
particles, the delocalization resonances occur also in the purely random
potential. This means, in particular, that in the one-dimensional case, not all
the states of the massive Dirac particles are localized in the presence of weak
disorder.
