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

The formula derived by Meir and Wingreen [Phys. Rev. Lett. 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 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 this 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.

Figure 1

Schematic diagram of the system used to derive the current formula. Before the coupling between the three regions is established, the leads are in equilibrium with chemical potentials ${\mu }_L$ and ${\mu }_R$, respectively. Upon coupling a current, $I$, starts to flow as the system approaches a common equilibrium. Interactions are allowed inside the central region $\left(C\right)$.