Electron transport through an interacting region: The case of a nonorthogonal basis set

TL;DR

This paper extends the Meir-Wingreen formula for electron current to nonorthogonal basis sets, enabling more accurate modeling of interacting regions in quantum transport using Green's functions and the Keldysh formalism.

Contribution

It generalizes the current formula to nonorthogonal basis sets, incorporating interactions and dual basis transformations within the Green's function framework.

Findings

Derived a nonorthogonal basis current formula using Green's functions.

Established a perturbation series for interactions in nonorthogonal basis.

Enabled more accurate quantum transport calculations with complex basis sets.

Abstract

The formula derived by Meir and Wingreen [Phys. Rev. Lett. {\bf 68}, 2512 (1992)] for the electron current through a confined, central region containing interactions is generalized to the case of a nonorthogonal basis set. As in the original work, the present derivation is based on the nonequilibrium Keldysh formalism. By replacing the basis functions of the central region by the corresponding elements of the dual basis, the lead- and central region-subspaces become mutually orthogonal. The current formula is then derived in the new basis, using a generalized version of second quantization and Green's function theory to handle the nonorthogonality within each of the regions. Finally, the appropriate nonorthogonal form of the perturbation series for the Green's function is established for the case of electron-electron and electron-phonon interactions in the central region.