An article describing how the extended Hückel model in ATK-SE works has been published in PRB.

The article contains a detailed description about how the Hückel model has been adapted for transport calculations, in particular the inclusion of a Hartree term for coupling to the electrostatic potential of gate electrodes and dielectric regions. 

Two examples of how the method can be applied are presented in the article:

A calculation of the transport properties of a Tour wire, which turns out to be better described by the Hückel model than DFT, when comparing to experimental results.	A study of a z-shaped graphene nano-transistor (similar to that considered by Q. Yan et al.), which exhibits an interesting transition from tunneling transport to thermionic emission as the central part is made longer.

This article serves as the fundamental reference for the extended Hückel model as implemented in ATK, and should be cited in any publication that makes use of this method.

The full reference is

Kurt Stokbro, Dan Erik Petersen, Søren Smidstrup, Anders Blom, Mads Ipsen, and Kristen Kaasbjerg,
Semiempirical model for nanoscale device simulations,
Physical Review B 82(7), 075420 (2010).

The article can be obtained from APS via doi:10.1103/PhysRevB.82.075420, and it can also be downloaded in preprint format from arXiv:1004.2812v1 [cond-mat.mes-hall].