Ab-initio formulation of the 4-point conductance of interacting electronic systems

TL;DR

This paper derives a fundamental expression for the 4-point conductance of interacting electronic systems, linking it to the density response function and simplifying its measurement in systems with barriers or constrictions.

Contribution

It introduces an ab-initio formulation for 4-point conductance using density response functions, connecting it to the 2-point conductance and identifying key exchange-correlation kernels.

Findings

4-point conductance equals 2-point conductance in certain interacting systems.

Formulation enables practical calculations for metal-vacuum-metal interfaces.

Identifies the exchange-correlation kernel relevant for conductance within TDDFT.

Abstract

We derive an expression for the 4-point conductance of a general quantum junction in terms of the density response function. Our formulation allows us to show that the 4-point conductance of an interacting electronic system possessing either a geometrical constriction and/or an opaque barrier becomes identical to the macroscopically measurable 2-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 implementationof our formula for a metal-vacuum-metal interface.