First-Principles electronic transport calculations in finite elongated systems: A divide and conquer approach

We present a \textit{first-principles} method for the evaluation of the transmittance probability and the coherent conductance through \textit{finite-elongated} systems composed of a repeating molecular unit and terminated at both ends. Our method is based on a divide and conquer approach in which the Hamiltonian of the elongated system can be represented by a block tridiagonal matrix, and therefore can be readily inverted. This allows us to evaluate the transmittance and the conductance using first-principles electronic structure methods without explicitly dealing with calculations involving the entire system. A proof of concept model based on a \textit{trans}-polyacetylene chain bridging two aluminum leads indicates that our divide and conquer approach is able to capture all of the features appearing in the transmittance probability curves of a full scale calculation. Using our method we investigate the edge effects on the electronic structure of finite sized carbon nanotubes as a function of their length and identify the limit at which the electronic structure converges to that of an infinite system.