  We show that the Nielsen-Ninomiya no-go theorem still holds on Floquet
lattice: there is an equal number of right-handed and left-handed Weyl points
in 3D Floquet lattice. However, in the adiabatic limit, where the time
evolution of low-energy subspace is decoupled from the high-energy subspace, we
show that the bulk dynamics in the low-energy subspace can be described by
Floquet bands with purely left/right-handed Weyl points, despite the no-go
theorem. For the adiabatic evolution of two bands, we show that the difference
of the number of right-handed and left-handed Weyl points equals twice the
winding number of the Floquet operator of the low-energy subspace over the
Brillouin zone, thus guaranteeing the number of Weyl points to be even. Based
on this observation, we propose to realize purely left/right-handed Weyl points
in the adiabatic limit using a Hamiltonian obtained through dimensional
reduction of four-dimensional quantum Hall system. We address the breakdown of
the adiabatic limit on the surface due to the presence of gapless boundary
states. This effect induces a circular motion of a wave packet in an applied
magnetic field, travelling alternatively in the low-energy and high-energy
subspace of the system.
