Invariants of the single-impurity Anderson model and implications for conductance functionals

F. Evers; P. Schmitteckert

doi:10.1209/0295-5075/103/47012

All issues

Volume 103 / No 4 (August 2013)

EPL, 103 4 (2013) 47012

Abstract

Issue		EPL Volume 103, Number 4, August 2013


Article Number		47012
Number of page(s)		5
Section		Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties
DOI		https://doi.org/10.1209/0295-5075/103/47012
Published online		16 September 2013

EPL, 103 (2013) 47012

Invariants of the single-impurity Anderson model and implications for conductance functionals

F. Evers¹^,2^,3 and P. Schmitteckert¹^,3

¹ Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT) - D-76021 Karlsruhe, Germany, EU
² Institut für Theorie der Kondensierten Materie, KIT - D-76128 Karlsruhe, Germany, EU
³ DFG- Center for Functional Nanostructures, KIT - D-76131 Karlsruhe, Germany, EU

Received: 3 June 2013
Accepted: 12 August 2013

Abstract

An exact relation between the conductance maximum G₀ at zero temperature and a ratio of lead densities is derived within the framework of the single-impurity Anderson model: $G_0={\mathfrak R}[n] \frac{2e^2}{h}$ , where ${\mathfrak R}[n]=4\Delta N_{{\cal L},x} \Delta N_{{\cal R},x}/(\Delta N_{{\cal L},x}+\Delta N_{{\cal R},x})^2$ and $\Delta N_{{\cal L},x}$ , $\Delta N_{{\cal R},x}$ denote the excess density in the left/right lead at distance x due to the presence of the impurity at the origin, x = 0. The relation constitutes a parameter-free expression of the conductance of the model in terms of the ground-state density that generalizes an earlier result to the generic case of asymmetric lead couplings. It turns out that the specific density ratio, ${\mathfrak R}[n]$ , is independent of the distance to the impurity x, the (magnetic) band structure and filling fraction of the contacting wires, the strength of the onsite interaction, the gate voltage and the temperature. Disorder-induced backscattering in the contacting wires has an impact on ${\mathfrak R}$ that we discuss. Our result suggests that it should be possible, in principle, to determine experimentally the peak conductance of the Anderson impurity by performing a combination of measurements of ground-state densities.

PACS: 71.15.Mb – Density functional theory, local density approximation, gradient and other corrections / 85.65.+h – Molecular electronic devices

© EPLA, 2013

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