Effect of a Coulombic dot-lead coupling on the dynamics of a quantum dot

TL;DR

This paper investigates how Coulombic interactions between a quantum dot and its leads influence the dot's dynamics, providing exact and approximate solutions for different lead dimensionalities.

Contribution

It offers a formally exact solution for a quantum dot coupled to a Luttinger liquid and an approximate RPA solution for metallic leads, clarifying Coulomb effects on dot dynamics.

Findings

Coulomb interactions cancel out in 2D and 3D leads, making dynamics similar to non-interacting cases.

In 1D leads, Coulomb interactions enhance dot-lead mixing.

Explicit short-time dynamics results are provided.

Abstract

The effect of a Coulombic coupling on the dynamics of a quantum dot hybridized to leads is determined. The calculation treats the interaction between charge fluctuations on the dot and the dynamically generated image charge in the leads. A formally exact solution is presented for a dot coupled to a Luttinger liquid and an approximate solution, equivalent to treating the lead dynamics within a random phase approximation, is given for a dot coupled to a two- or three-dimensional metallic lead. The leading divergences arising from the long-ranged Coulomb interaction are found to cancel, so that in the two- and three-dimensional cases the quantum-dot dynamics is equivalent to that obtained by neglecting both the dot-lead Coulomb coupling and the Coulomb renormalization of the lead electrons, while in the one-dimensional case the dot-lead mixing is enhanced relative to the non-interacting case. Explicit results are given for the short-time dynamics.