Quantum transport in a one-dimensional quantum dot array

In this paper we study electronic transport through a quantum dot array containing an arbitrary number of quantum dots connected in a series by tunnel coupling under dc bias. The on-site Coulomb interaction is ignored. The retarded self-energy of any dot in the array is made up of left and right components and is of staircase type, terminating at corresponding electron reservoirs. We calculate the dc current based on the nonequilibrium Green’s function formalism developed by Jauho et al. [A.-P. Jauho, Ned S. Wingreen, and Y. Meir, Phys. Rev. B 50, 5528 (1994)]. The dc current in both finite and infinite number dots in the array is calculated. The electronic spectrum of the system is found to fall within an interval centered at ${\epsilon }_0$ (the dot energy level) with a width of two times the tunnel coupling amplitude between two neighboring dots. The electronic charge in each dot is plotted for the finite number dot array.