Figure 1

Sketch of a tunneling device including left ($\mathcal{L}$) and right ($\mathcal{R}$) leads and a contact region ($\mathcal{C}$) in between. The vertical dotted lines mark the interface between the subsystems and the arrows indicate the coupling potential.Reuse & Permissions

Figure 2

Principal sketch of the decoupling through buffer regions in tunnel junctions. In (b) and (d), the corresponding picture by cutting bonds between atomic sites is shown. In (a) and (c), a repulsive potential is introduced that demonstrates the decoupling via a layer “removal” at the corresponding atomic sites.Reuse & Permissions

Figure 3

Local density of states for a bulk system without external applied bias using (a) the spectral function and (b) the lesser Green's function within our KKR method.Reuse & Permissions

Figure 4

(a) Comparison of the local density of states at the boundary ($z/a=6$) and in the middle of the scattering region ($z/a=20$) for a bulk system (without applied bias voltage) as function of the imaginary part of the energy using the difference of retarded and advanced Green function (EQ), and using the Keldysh expression (NEQ) within our KKR method. (b) The relative change of the LDOS between the Keldysh expression with respect to the spectral function.Reuse & Permissions

Figure 5

Transmission coefficients in the first Brillouin zone at the corresponding Fermi energies for different bulk systems using the formula given by Baranger and Stone (a) and the Caroli-type expression (b). The deviation of the transmission coefficients from the nearest integer number for the results obtained by the Baranger-Stone formula (c) and the Caroli-type expression (d). The numbers in the insets of the figures in (d) are values used for magnification of their corresponding deviations. The high symmetry points are $\overline{\Gamma }$ in the center, $\overline{\mathrm{M}}$ in the corners, and $\overline{\mathrm{X}}$ in the center of the faces of the Brillouin zone [see rightmost figure in (a)].Reuse & Permissions

Figure 6

Cell-integrated induced charge density (a) and induced change in the effective potential (b) for Li/Vac/Li. The density is normalized to the surface area and the external potential is averaged with respect to the surface plane.Reuse & Permissions

Figure 7

Induced charge per area for (the left electrode) and capacitance as a function of bias voltage for Li/Vac/Li.Reuse & Permissions

Figure 8

Leakage current-voltage and conductance-voltage characteristic of for Li/Vac/Li.Reuse & Permissions

Figure 9

Contributions to current and conductance densities for different bias voltages within the Brillouin zone for Li/Vac/Li. The high symmetry points are $\overline{\Gamma }$ in the center, $\overline{\mathrm{M}}$ in the corners, and $\overline{\mathrm{X}}$ in the center of the faces of the Brillouin zone [see rightmost figure in (a)].Reuse & Permissions

Figure 10

Sketch of energy contours using either a (a) nonvanishing or (c) a vanishing “technical” temperature. In (b) and (d), the Fermi-Dirac distribution weights for the particular energy intervals including or excluding temperature are shown. The quantities ${\mu }_{<}=\min ({\mu }_{\mathcal{L}},{\mu }_{\mathcal{R}})$ and ${\mu }_{>}=\max ({\mu }_{\mathcal{L}},{\mu }_{\mathcal{R}})$ refer to both chemical potentials.Reuse & Permissions

Figure 11

Local density of states for a free electrons without external applied bias and their different contributions to the LDOS within a finite differences method.Reuse & Permissions