Gate-dependent tunneling-induced level shifts observed in carbon nanotube quantum dots

TL;DR

This paper investigates how gate-dependent tunneling affects energy level shifts in carbon nanotube quantum dots, revealing asymmetric cotunneling and Coulomb diamond variations explained by second-order perturbation theory.

Contribution

It provides a detailed analysis of tunneling renormalization effects and environment-induced level shifts in carbon nanotube quantum dots using experimental data and theoretical modeling.

Findings

Asymmetric gate dependence of inelastic cotunneling lines observed.

Systematic gate dependence of Coulomb diamond size and shape.

Second-order perturbation theory explains tunneling-induced level shifts.

Abstract

We have studied electron transport in clean single-walled carbon nanotube quantum dots. Because of the large number of Coulomb blockade diamonds simultaneously showing both shell structure and Kondo effect, we are able to perform a detailed analysis of tunneling renormalization effects. Thus determining the environment induced level shifts of this artificial atom. In shells where only one of the two orbitals is coupled strongly, we observe a marked asymmetric gate-dependence of the inelastic cotunneling lines together with a systematic gate dependence of the size (and shape) of the Coulomb diamonds. These effects are all given a simple explanation in terms of second-order perturbation theory in the tunnel coupling.