  Profiles of the spin and orbital angular momentum accumulations induced by a
longitudinally applied electric field are explored in nanoribbons of $p$-band
systems with a honeycomb lattice. We show that nanoribbons with zigzag borders
can exhibit orbital magnetoelectric effects. More specifically, we have found
that purely orbital magnetization may be induced in these systems by means of
this external electric field. The effect is rather general and may occur in
other two-dimensional multi-orbital materials. Here, it requires the presence
of both spin-orbit interaction and sub-lattice symmetry breaking to manifest.
