Quantum conductance of homogeneous and inhomogeneous interacting electron systems

We obtain the conductance of a system of electrons connected to leads, within time-dependent density-functional theory, using a direct relation between the conductance and the density response function. Corrections to the non-interacting conductance appear as a consequence of the functional form of the exchange-correlation kernel at small frequencies and wavevectors. The simple adiabatic local-density approximation and non-local density-terms in the kernel both give rise to significant corrections in general. In the homogeneous electron gas, the former correction remains significant, and leads to a failure of linear-response theory for densities below a critical value.Comment: for resolution of the here published results see Phys. Rev. B 76, 125433 (2007

Comment on "Dynamical corrections to the DFT-LDA electron conductance in nanoscale systems"

In a recent paper Sai et al. [1] identified a correction R^{dyn}$to the DC conductance of nanoscale junctions arising from dynamical exchange-correlation (XC) effects within time-dependent density functional theory. This quantity contributes to the total resistance through$R=R_{s}+R^{dyn}$where$R_{s}$is the resistance evaluated in the absence of dynamical$XC$effects. In this Comment we show that the numerical estimation of$R^{dyn}$ in example systems of the type they considered should be considerably reduced, once a more appropriate form for the shear electron viscosity ¿ is used

Ab initio formulation of the four-point conductance of interacting electronic systems

We derive an expression for the four-point conductance of a general quantum junction in terms of the density response function. Our formulation allows us to show that the four-point conductance of an interacting electronic system possessing either a geometrical constriction and/or an opaque barrier becomes identical to the macroscopically measurable two-point conductance. Within time-dependent density-functional theory the formulation leads to a direct identification of the functional form of the exchange-correlation kernel that is important for the conductance. We demonstrate the practical implementation of our formula for a metal-vacuum-metal interface

Density functional calculations of nanoscale conductance

Density functional calculations for the electronic conductance of single molecules are now common. We examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradient-corrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, XC corrections to the current are missed by the standard methodology. For finite bias, a new methodology for performing calculations can be rigorously derived using an extension of time-dependent current density functional theory from the Schroedinger equation to a Master equation.Comment: topical review, 28 pages, updated version with some revision