  We investigate the effects of periodic fields and disorder on topological
properties of a Weyl-semimetal thin film. The two periodic fields, i.e., a
periodic magnetic field and elliptically polarized light, are discussed
respectively. By use of the Floquet theory, we find that both the two periodic
drives can resonantly induce the topological transitions from normal insulator
(NI) phases to Floquet topological insulator (FTI) phases. The Floquet
topological transitions are characterized by variation of Chern number.
Moreover, we show that the Floquet topological transitions can be explained by
a combination of the quantum well approximation and the rotating wave
approximation. In the disordered Weyl-semimetal thin film model under periodic
fields, we calculate the Bott index to characterize topological phase. It is
found that the FTI phase is robust against weak disorder, and collapses for
strong disorder strength. Interestingly, we find that disorder can also induce
a topological transition from a topological trivial phase to an FTI phase,
establishing the Floquet topological Anderson insulator (FTAI) phase. Finally,
an effective-medium theory based on the Born approximation further confirms the
numerical conclusions.
