Dynamical Correction to Linear Kohn-Sham Conductances from Static Density Functional Theory

For molecules weakly coupled to leads the exact linear Kohn-Sham (KS) conductance can be orders of magnitude larger than the true linear conductance due to the lack of dynamical exchange-correlation (xc) corrections. In this work we show how to incorporate dynamical effects in KS transport calculations. The only quantity needed is the static xc potential in the molecular junction. Our scheme provides a comprehensive description of Coulomb blockade without breaking the spin symmetry. This is explicitly demonstrated in single-wall nanotubes where the corrected conductance is in good agreement with experimental data whereas the KS conductance fails dramatically.

Figure 1

Top: electron number $N$ versus gate in MB and DFT (indistinguishable) for a single level coupled to featureless leads with $U=10$, $\mu =0$ at various temperatures $T$ (all energies in units of $\gamma$). For these parameters $T_{\mathrm{K}}=\sqrt{U\gamma }\exp (-(\pi U/8\gamma ))\simeq 0.06$. Bottom: $G$ from Eq. (2) (solid line) and $G_s$ from Eq. (4) (dashed line) in units of $G_0=2e^2/h$.

Figure 2

Linear conductance from Eq. (2) using the spectral function Eq. (3) (MB, solid line) and from Eq. (12) (TDDFT, dashed line). The inset shows a comparison between the exact and the approximate $R$. Same parameters as in Fig. 1.

Figure 3

Linear conductance from Eq. (4) (KS, dashed line) and from Eq. (12) (TDDFT, solid line) for the HOMO-LUMO model with diagonal and off-diagonal $\Gamma$ matrices (left axis) and KS energies ${ϵ}_{H/L}={ϵ}_{0H/L}+{\overline{v}}_{\mathrm{Hxc}}$ (right axis). The electron number $N$ for different ranges of $v$ is also indicated.

Figure 4

Linear KS and TDDFT conductance [Eq. (12)] for a SWNT quantum dot in comparison to experimental conductance from Ref. [24], as function of gate voltage $v_g$.