Compressibility, capacitance and ground state energy fluctuations in a weakly interacting quantum dot

TL;DR

This paper investigates how electron-electron interactions influence the compressibility, capacitance, and energy fluctuations in weakly interacting quantum dots, combining analytical and numerical methods for comprehensive insights.

Contribution

It provides a detailed analysis of interaction effects on quantum dot properties using the random-phase approximation and numerical models, highlighting fluctuation suppression.

Findings

Compressibility and capacitance decrease with interaction strength

Fluctuations of these quantities are significantly suppressed by interactions

Analytical and numerical results show excellent agreement for weak interactions

Abstract

We study the effect of electron-electron (e-e) interactions on compressibility, capacitance and inverse compressibility of electrons in a quantum dot or a small metallic grain. The calculation is performed in the random-phase approximation. As expected, the ensemble-averaged compressibility and capacitance decreases as a function of the interaction strength, while the mean inverse compressibility increases. Fluctuations of the compressibility are found to be strongly suppressed by the e-e interactions. Fluctuations of the capacitance and inverse compressibility also turn out to be much smaller than their averages. The analytical calculations are compared with the results of a numerical calculation for the inverse compressibility of a disordered tight-binding model. Excellent agreement for weak interaction values is found. Implications for the interpretation of current experimental data are discussed.