It is based on the nonequilibrium Green's function formalism, see
- The book by S. Datta on Electronic Transport in Mesoscopic Systems,
https://books.google.dk/books/about/Electronic_Transport_in_Mesoscopic_Syste.html?id=28BC-ofEhvUC&redir_esc=y;- The tutorials (and references therein) on the NEGF and electron transport in QuantumATK at
https://docs.quantumwise.com/manuals/NEGF.html and
https://docs.quantumwise.com/tutorials/atk_transport_calculations/atk_transport_calculations.html;- The ATK-transport reference paper on "Density-functional method for nonequilibrium electron transport" by Mads Brandbyge, José-Luis Mozos, Pablo Ordejón, Jeremy Taylor, and Kurt Stokbro, Phys. Rev. B 65, 165401 – Published 22 March 2002.
- If you are interested in how this formalism is related to the Landauer-Buttiker approach based on wave function formalism, you may also have a look at "Conductance calculations for quantum wires and interfaces: Mode matching and Green’s functions", P. A. Khomyakov, G. Brocks, V. Karpan, M. Zwierzycki, and P. J. Kelly, Phys. Rev. B 72, 035450 – Published 19 July 2005; "Krylov subspace method for evaluating the self-energy matrices in electron transport calculations", Hans Henrik B. Sørensen, Per Christian Hansen, Dan Erik Petersen, Stig Skelboe, and Kurt Stokbro, Phys. Rev. B 77, 155301 – Published 1 April 2008.
