Addition Spectra of Chaotic Quantum Dots: Interplay between Interactions and Geometry

TL;DR

This study explores how interactions and geometry influence the ground states of chaotic quantum dots, revealing a transition from random matrix behavior to charge rearrangement effects that depend on dot shape and size.

Contribution

It demonstrates a crossover in interaction regimes affecting charge fluctuations, highlighting the role of geometry and interactions in quantum dot behavior.

Findings

Weak interactions follow random matrix predictions for charge fluctuations.

Strong interactions cause charge rearrangements and enhanced fluctuations.

Charge ordering effects depend on dot shape and size.

Abstract

We investigate the influence of interactions and geometry on ground states of clean chaotic quantum dots using the self-consistent Hartree-Fock method. We find two distinct regimes of interaction strength: While capacitive energy fluctuations $\delta \chi$ follow approximately a random matrix prediction for weak interactions, there is a crossover to a regime where $\delta \chi$ is strongly enhanced and scales roughly with interaction strength. This enhancement is related to the rearrangement of charges into ordered states near the dot edge. This effect is non-universal depending on dot shape and size. It may provide additional insight into recent experiments on statistics of Coulomb blockade peak spacings.