# Why is the Nonequilibrium Green’s function (NEGF) method for quantum transport not implemented in plane wave codes like VASP and Quantum Espresso?

DFT codes like Siesta, QuantumATK, Questaal, and Smeagol having localized basis sets have NEGF implementations available. But not in plane wave codes like VASP and Quantum Espresso. Why is it so?

• I'm interested! – Nike Dattani May 5 '20 at 4:03
• Do you mean GW-type or RPA-type post DFT calculation? I believe both GW-type and RPA-type can be understood from NEGF. – Yingzhou Li May 5 '20 at 17:25
• I just keep thinking the huge type of hardware resources QE will need to do transport calculations using plane-waves. – Camps May 12 '20 at 16:58
• I think this is answered, could you mark it answered? – zeroth Nov 11 '20 at 9:46

Since VASP relies on a non-localized basis set (plane waves), it is not possible to implement a non-equilibrium Green's function approach directly. The NEGF approach can be easily expressed using a localized basis set where you can define local Hamiltonians and local Green's Functions. In the transmission function for a device with N layers, you have terms, $$G^R_{1N}$$ and $$G^{A}_{N1}$$, which you can think of as a measure of the ability for electrons to travel between layer 1 to layer N. This spatial information falls out naturally with a localized basis set. This is why codes like Siesta, QuantumATK, Questaal, and Smeagol all use localized basis sets for their NEGF codes.