How sharply does the Anderson model depict a single-electron transistor?

TL;DR

This paper evaluates how well the Anderson model captures the low-temperature transport properties of single-electron transistors, highlighting its strengths in universal features and limitations in non-universal details.

Contribution

It demonstrates that the Anderson model accurately reproduces universal low-energy properties but cannot quantitatively capture non-universal features, emphasizing the need for high-energy b initio studies.

Findings

Universal mapping fits experimental data very accurately.

Dot occupation and asymmetry parameter are less accurate.

Non-universal features are not quantitatively reproduced.

Abstract

The single-impurity Anderson model has been the focus of theoretical studies of molecular junctions and the single-electron transistor, a nanostructured device comprising a quantum dot that bridges two otherwise decoupled metallic leads. The low-temperature transport properties of the model are controlled by the ground-state occupation of the quantum dot, a circumstance that recent density-functional approaches have explored. Here we show that the ground-state dot occupation also parametrizes a linear mapping between the thermal dependence of the zero-bias conductance and a universal function of the temperature scaled by the Kondo temperature. Careful measurements by Grobis and co-workers are very accurately fitted by the universal mapping. Nonetheless, the dot occupation and an asymmetry parameter extracted from the same mapping are relatively distant from the expected values. We conclude that mathematical results derived from the model Hamiltonian reproduce accurately the universal physical properties of the device. In contrast, non-universal features cannot be reproduced quantitatively. To circumvent this limitation, \emph{ab initio} studies of the device at high energies seem necessary, to accurately define the model Hamiltonian. Our conclusion reinforces findings by Gross and coworkers, who applied time-dependent density-functional theory to show that, to describe the low-energy properties of molecular junctions, one must be able to describe the high-energy regime.