Quantum transport through the edge states of Zigzag phosphorene nanoribbons in presence of a single point defect: analytic Green's function method

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.