Density functional description of Coulomb blockade: Adiabatic versus dynamic exchange correlation

Above the Kondo temperature, the Kohn-Sham zero-bias conductance of an Anderson junction has been shown to completely miss the Coulomb blockade. Within a standard model for the spectral function, we deduce a parametrization for both the on-site exchange-correlation potential and the bias drop as a function of the site occupation that applies for all correlation strengths. We use our results to sow doubt about the common interpretation of such corrections as arising from dynamical exchange-correlation contributions.

Figure 1

Upper panel: Conductance $T$ as a function of $(\mu -\varepsilon )/U$, plotted in units of $G_0=2e^2/h=1/\pi$, the conductance quantum. Lower panel: $n$ as a function of $(\mu -\varepsilon )/U$. Different $u=U/\mathrm{\Gamma }$ are used.

Figure 2

$v_{\mathrm{HXC}}\left[n\right]$ as a function of $n$ for various $u=U/\mathrm{\Gamma }$. Solid lines are results from Eq. (7) with $n$ calculated from Eq. (3); dashed lines are the approximation of Eq. (8).

Figure 3

Physical conductance (solid lines) from Eq. (4) and KS conductance (dashed lines) for various values of $u=U/\mathrm{\Gamma }$, plotted in units of $G_0=2e^2/h=1/\pi$, the conductance quantum.

Figure 4

$\delta V_{\mathrm{S}}^{\mathrm{app}}$ as a function of $n$ for various correlation strengths $u=U/\mathrm{\Gamma }$. Solid lines are “exact,” as defined by Eq. (12). Dashed lines are approximate, as in Eq. (11).

Figure 5

Solid lines: Physical conductances from Eq. (4). Dashed lines: Conductances using approximations for both the local HXC potential, Eq. (8), and the nonlocal XC bias, Eq. (11).

Figure 6

$\delta V_{\mathrm{XC}}$ as a function of $\mu$ for various correlation strengths $u=U/\mathrm{\Gamma }$. Solid lines are “exact” as defined by Eq. (12) and dashed lines are approximations using both Eqs. (11) and (8).

Figure 7

Upper panel: Conductance $T$ as a function of $(\mu -\varepsilon )/U$, plotted in units of $G_0$, for different temperatures $\tau$ at a fixed $u=U/\mathrm{\Gamma }=10$. Solid lines are “exact” and dashed lines are (uncorrected) KS conductance. The black line is for the low-temperature limit and is the same as the red line in Fig. 1. Lower panel: $n$ as a function of $(\mu -\varepsilon )/U$. By definition, the KS occupation always matches that of the exact occupation at all temperatures.

Figure 8

Finite temperature generalization of Fig. 4 (but with $\delta V_{\mathrm{XC}}$ plotted instead of $\delta V_{\mathrm{S}}$): $\delta V_{\mathrm{XC}}$ as a function of $n$, for different temperatures $\tau$ at a fixed $u=U/\mathrm{\Gamma }=10$. Black line is the low-temperature limit result.