  Topological insulators in three dimensions are characterized by a Z2-valued
topological invariant, which consists of a strong index and three weak indices.
In the presence of disorder, only the strong index survives. This paper studies
the topological invariant in disordered three-dimensional system by viewing it
as a super-cell of an infinite periodic system. As an application of this
method we show that the strong index becomes non-trivial when strong enough
disorder is introduced into a trivial insulator with spin-orbit coupling,
realizing a strong topological Anderson insulator. We also numerically extract
the gap range and determine the phase boundaries of this topological phase,
which ?ts well with those obtained from self-consistent Born approximation
(SCBA) and the transport calculations.
