Quantum transport calculations: An effective medium theory based on the projector augmented wave method with the plane-wave basis

We present an effective medium theory--plane-wave (EMT-PW) based on density functional theory (DFT) that is implemented in vasp using the projector augmented-wave method with a plane-wave basis set. The transmission coefficient, $\ensuremath{\tau}(E)$, is derived through three complementary approaches: the current density relation $J=nqv$, the field operator method, and the nonequilibrium Green's function (NEGF) formalism. We compare $\ensuremath{\tau}(E)$ calculated using EMT-PW with results from NEGF-DFT, based on the NanoDCAL package utilizing a linear combination of atomic orbitals basis set, for both periodic and nonperiodic boundary conditions. The minor discrepancies observed are attributed to differences in basis sets, pseudopotentials, and the treatment of lead regions. Notably, the EMT-PW framework avoids the common issue of overcompleteness encountered in nonequilibrium transport theories and allows for the decomposition of the total transmission coefficient into contributions from individual eigenstates, providing an alternative approach to calculate transport properties through nanoscale systems.