Dynamical Coulomb Blockade and the Derivative Discontinuity of Time-Dependent Density Functional Theory

The role of the discontinuity of the exchange-correlation potential of density functional theory is studied in the context of electron transport and shown to be intimately related to Coulomb blockade. By following the time evolution of an interacting nanojunction attached to biased leads, we find that, instead of evolving to a steady state, the system reaches a dynamical state characterized by correlation-induced current oscillations. Our results establish a dynamical picture of Coulomb blockade manifesting itself as a periodic sequence of charging and discharging of the nanostructure.

Figure 1

Time evolution of the density, current, and KS potential for three different biases. In all panels, the solid, chain, and dashed lines refer to $W_L=1.3$, 1.6, 1.9, respectively. Top panel: densities at the QD. The inset shows the density at the end of the propagation period. Middle three panels: current through the QD (thick lines) and KS potential (thin lines). Bottom panel: current five sites away from the QD.

Figure 2

Left panel: Graphical solution of Eq. (8) for few values of the applied bias $W_L$. Right panel: Steady-state density as function of $W_L$ for a smoothened $v_{\mathrm{KS}}$ ($a={10}^{-4}$) and few values of the dot-lead hopping $V_{\mathrm{link}}$.