  We study a scattering on an ultra-low potential in zigzag graphene
nanoribbon. Using mathematical framework based on the continuous Dirac model
and augumented scattering matrix, we derive a condition for the existence of a
trapped mode. We consider the threshold energies where the continuous spectrum
changes its multiplicity and show that the trapped modes may appear for
energies slightly less than a threshold and its multiplicity does not exceeds
one. We prove that trapped modes do not appear outside the threshold, provided
the potential is sufficiently small.
