Energy Level Statistics of Quantum Dots

TL;DR

This paper explores how disorder and interactions affect the energy level statistics in quantum dots, revealing Poisson, Wigner-Dyson, and Gaussian regimes with broad crossover behaviors, including a two-sided exponential distribution.

Contribution

It provides a comprehensive numerical analysis of energy level statistics across different regimes in disordered quantum dots, highlighting crossover phenomena and potential experimental relevance.

Findings

Poisson statistics at strong disorder

Wigner-Dyson statistics at weak disorder and interactions

Gaussian intermediate regime with broad crossover behaviors

Abstract

We investigate the charging energy level statistics of disordered interacting electrons in quantum dots by numerical calculations using the Hartree approximation. The aim is to obtain a global picture of the statistics as a function of disorder and interaction strengths. We find Poisson statistics at very strong disorder, Wigner- Dyson statistics for weak disorder and interactions, and a Gaussian intermediate regime. These regimes are as expected from previous studies and fundamental considerations, but we also find interesting and rather broad crossover regimes. In particular, intermediate between the Gaussian and Poisson regimes we find a two-sided exponential distribution for the energy level spacings. In comparing with experiment, we find that this distribution may be realized in some quantum dots.