  The toroidal states in $^{28}$Si with spin extending to extremely high are
investigated with the cranking covariant density functional theory on a 3D
lattice. Thirteen toroidal states with spin $I$ ranging from 0 to 56$\hbar$ are
obtained, and their stabilities against particle emissions are studied by
analyzing the density distributions and potentials. The excitation energies of
the toroidal states at $I=28$, 36, 44$\hbar$ reasonably reproduce the observed
three resonances extracted from the 7-$\alpha$ de-excitation of $^{28}$Si. The
$\alpha$ clustering of these toroidal states is supported by the
$\alpha$-localization function.
