  Zigzag phosphorene nanoribbons have quasi-flat band edge modes entirely
detached from the bulk states. We analytically study the electronic transport
through such edge states in the presence of a localized defect for
semi-infinite and finite ribbons. Using the tight-binding model, we derive
analytical expressions for the Green's function and transmission amplitude of
both pristine and defective nanoribbons. We find that the transmission of both
semi-infinite and finite ribbons is sensitive to the location of a single
impurity defect with respect to the edge. By the presence of an impurity on the
outermost edge site of the ribbon, the transmission through the edge channel,
similar to a one-dimensional chain, strongly suppresses for the entire energy
spectrum of the quasi-flat band. In contrast, the transmission of low-energy
$(E\approx 0)$ states, is robust as the impurity is moved one position far away
from the edge on the same sub-lattice. The analytical calculations are also
complemented by exact numerical transport computations using the Landauer
approach.

Disordered Systems and Neural Networks;Mesoscale and Nanoscale Physics;Materials Science