  Anderson localization, the absence of diffusive transport in disordered
systems, has been manifested as hopping transport in numerous electronic
systems, whereas in recently discovered topological insulators it has not been
directly observed. Here we report experimental demonstration of transition from
diffusive transport in the weak antilocalization regime to variable range
hopping transport in the Anderson localization regime with ultrathin
(Bi$_{1-x}$Sb$_x$)$_2$Te$_3$ films. As disorder becomes stronger, negative
magnetoconductivity due to the weak antilocalization is gradually suppressed,
and eventually positive magnetoconductivity emerges when the electron system
becomes strongly localized. This works reveals the critical role of disorder in
the quantum transport properties of ultrathin topological insulator films, in
which theories have predicted rich physics related to topological phase
transitions.
