Fluctuation of inverse compressibility for electronic systems with random capacitive matrices

TL;DR

This paper models the fluctuations in Coulomb blockade peak spacings in large quantum dots using a classical electrostatic approach with random capacitive matrices, explaining experimental phenomena like closely spaced peaks.

Contribution

It introduces a classical model with random capacitive couplings to study peak spacing fluctuations in large quantum dots, capturing effects not explained by single-island models.

Findings

Distribution peaks at small spacings, unlike Gaussian in single-island models

Model explains occurrence of closely spaced Coulomb peaks

Qualitative match with experimental peak behavior under magnetic fields

Abstract

This article is concerned with statistics of addition spectra for systems of identical charged particles. A classical model is suggested in order to study fluctuations of Coulomb blockade peak spacings in large two-dimensional semiconductor quantum dots. It is based on the electrostatics of several electron islands among which there are random inductive and capacitive couplings. Each island can accommodate electrons on quantum orbitals whose energy depend also on an external magnetic field. | In contrast with a single island quantum dot where the spacing distribution between conductance peaks is close to Gaussian, here the distribution has a peak at small spacing value. The fluctuations are mainly due to charging effects. The model can explain the occasional occurrence of couples or even triples of closely spaced Coulomb blockade peaks, as well as the qualitative behavior of peak positions with the applied magnetic field.