Motivated by the recent experimental success in realizing synthetic
spin-orbit coupling in ultracold atomic systems, we consider N-component atoms
coupled to a non-Abelian SU(N) gauge field. More specifically, we focus on the
case, referred to here as "SU(3) spin-orbit-coupling," where the internal
states of three-component atoms are coupled to their momenta via a matrix
structure that involves the Gell-Mann matrices (in contrast to the Pauli
matrices in conventional SU(2) spin-orbit-coupled systems). It is shown that
the SU(3) spin-orbit-coupling gives rise to qualitatively different phenomena
and in particular we find that even a homogeneous SU(3) field on a simple
square lattice enables a topologically non-trivial state to exist, while such
SU(2) systems always have trivial topology. In deriving this result, we first
establish an exact equivalence between the Hofstadter model with a 1/N Abelian
flux per plaquette and a homogeneous SU(N) non-Abelian model. The former is
known to have a topological spectrum for N>2, which is thus inherited by the
latter. It is explicitly verified by an exact calculation for N=3, where we
develop and use a new algebraic method to calculate topological indices in the
SU(3) case. Finally, we consider a strip geometry and establish the existence
of three gapless edge states -- the hallmark feature of such an SU(3)
topological insulator.Comment: 4.2 pages, 1 figur