Accelerated modeling of electron transport using Bloch waves*

In computational condensed matter, the modeling of quantum transport in nanoscaled structures has received considerable attention, driving the development of ever smaller and faster electronics.
Most full band models, that account for the complete bandstructure of the material, are based on the linear combination of localized atomic orbitals, in particular, the tight-binding (TB) approximation. On the other hand, fully delocalized plane wave methods have been used in highly accurate ab-initio codes. While plane waves are an excellent basis for quantum transport, they are limited by their prohibitive computational cost for larger structures.
We have developed a hybrid approach: by expanding on a select set of Bloch waves in slices of the system we capture the atomic-scale variation, while the large-scale envelope is described using a TB-like approach based on finite-elements. We have thus retained most of the benefits of the plane wave method while reducing the computational burden by at least two orders of magnitude. Furthermore, unlike TB, our method can directly use the ab-initio Bloch waves and doesn't require additional fitting.
We apply our method to structures that require quantum mechanical treatment but are inaccessible using plane wave methods.