Linear Chain of Coupled Quantum Dots

TL;DR

This paper studies a linear chain of spin-polarized quantum dots, analyzing electron interactions, energy levels, and conductance properties using quantum Monte Carlo methods, revealing complex correlated structures and limitations of Hartree-Fock theory.

Contribution

It introduces a detailed analysis of electron correlations and conductance in coupled quantum dot chains, highlighting the failure of Hartree-Fock approximation in this context.

Findings

Electron chemical potential follows a specific relation involving system parameters.

Multiple correlated electron structures are observed, including commensurate and incommensurate patterns.

Hartree-Fock theory does not accurately predict the electronic structures due to near-degenerate solutions.

Abstract

A linearly coupled chain of spin-polarized quantum dots is investigated under the condition that the number of electrons is equal to or less than the number of the dots. The chemical potential of the system, $\mu_{N}=E(N)-E(N-1)$, satisfies, $(\mu_{N}+\mu_{N_{\ell}+2-N)}/2 \approx V+2t (N, N_{\ell}, V, E(N)$ and $t$ are the number of electrons, the number of dots, and the strength of nearest neighbor electron-electron interactions, the total groundstate energy and the hopping integral between two adjacent dots). This property will be reflected in the spacing between the conductance peaks. The electron density structures are determined using a quantum Monte Carlo method. As the number of electrons is varied several correlated structures are found that are commensurate/incommensurate with the periodic dot system. Hartree-Fock theory fails to predict the correct electronic structures of this system because several nearly degenerate solutions exist.