Dynamical Corrections to the DFT-LDA Electron Conductance in Nanoscale Systems

Using time-dependent current-density functional theory, we derive analytically the dynamical exchange-correlation correction to the dc conductance of nanoscale junctions. The correction pertains to the conductance calculated in the zero-frequency limit of time-dependent density functional theory within the adiabatic local-density approximation. In particular, we show that in linear response, the correction depends nonlinearly on the gradient of the electron density; thus, it is more pronounced for molecular junctions than for quantum point contacts. We provide specific numerical examples to illustrate these findings.

Figure 1

Schematic of a nanoscale junction between electrodes with applied bias $V$. Because of dynamical XC effects there is an XC field which gives rise to an additional voltage drop $V^{\mathrm{dyn}}$ compared to the electrostatic potential difference.

Figure 2

Planar (dashed line) and macroscopic (solid line) averages of the charge density for a gold point contact (left) and a molecular junction (right).

Figure 3

The resistance due to dynamical effects as calculated from Eq. (14) with the charge density determined from DFT-LDA calculations as a function of the main parameters discussed in the text. The resistance of a gold point contact and a BDT molecular junction are indicated by dots.