Self-consistent non-equilibrium transport using plane waves

In this work, we present a detail description of a self-consistent ab initio procedure for modeling the non-equilibrium elastic electron transport through a nanostructure coupled to semi-infinite external electrodes and with a finite applied bias voltage. Our method is based on the approach presented in Wang [L.W. Wang, Phys. Rev. B 72 (2005) 045417] and Garcia-Lekue and Wang [A. Garcia-Lekue, L.W. Wang, Phys. Rev. B 72 (2005) 045417], where the coherent quantum transport is calculated by means of the exact scattering states with plane wave non-local pseudopotentials, using periodic boundary conditions. In our previous calculation, the charge density and the electron potential were not calculated self-consistently even for a finite bias problem. Here, we introduce an iterative approach to obtain the self-consistent charge density and potential. Our self-consistent algorithm employs Pulay–Kerker mixing scheme and is found to provide fast, accurate and stable numerical solutions of the non-equilibrium problem. Details of the method are presented thus the readers can implement the method easily. As an illustration of our method, non-equilibrium transport properties for a model system made up of a di-thiol-benzene molecule connected by two Cu wires are calculated.