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

Question

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?

Answer 1

I quote from Derek Stewart that gave the answer here:

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.

For plane wave codes like VASP, you have two options for calculating electronic transport. You can calculate the zero bias transmission of electrons using the scattering approach of Choi and Ihm (Phys. Rev. B, 59, 2267, 1999). Smogunov and Dal Corso did a nice job implementing this in the PWCOND code for Quantum Espresso (see Phys. Rev. B, 70, 045417 (2014)). However, I am not sure if this approach can be used at finite bias. The other route is to run the plane wave calculation and then map your results to a localized basis set using Wannier functions or some other tight-binding representation. This is done in the code WanT. However, with this route, you are always stuck with a two step process and you have to be careful that your mapping to the localized basis set is correct. So in the end, you may be better off going with a localized basis code for your transport calculations.