Electronic lifetimes in ballistic quantum dots electrostatically coupled to metallic environments

TL;DR

This paper investigates how the lifetime of low-energy electrons in a two-dimensional quantum dot varies with geometric and screening parameters, revealing different regimes including Fermi liquid, marginal Fermi liquid, and non-trivial power-law behaviors.

Contribution

It provides a comprehensive analysis of electronic lifetimes in quantum dots coupled to metallic environments, highlighting the conditions leading to various many-body behaviors.

Findings

Fermi liquid behavior when dot-gate distance is very short or very long.

Non-Fermi liquid behavior in unscreened dipole cases with small dots.

Power-law decay of level width with dot-gate distance in certain regimes.

Abstract

We calculate the lifetime of low-energy electronic excitations in a two-dimensional quantum dot near a metallic gate. We find different behaviors depending on the relative values of the dot size, the dot-gate distance and the Thomas-Fermi screening length within the dot. The standard Fermi liquid behavior is obtained when the dot-gate distance is much shorter than the dot size or when it is so large that intrinsic effects dominate. Departures from the Fermi liquid behavior are found in the unscreened dipole case of small dots far away from the gate, for which a Caldeira-Leggett model is applicable. At intermediate distances, a marginal Fermi liquid is obtained if there is sufficient screening within the dot. In these last two non-trivial cases, the level width decays as a power law with the dot-gate distance.