Determination of electron-hole correlation length in CdSe quantum dots using explicitly correlated two-particle cumulant

TL;DR

This paper introduces a new method to calculate the electron-hole correlation length in CdSe quantum dots using explicitly correlated wave functions and sum-rule conditions, revealing size-dependent effects.

Contribution

It presents a novel approach combining explicitly correlated Hartree-Fock calculations and sum-rule constraints to determine electron-hole correlation length in quantum dots.

Findings

Correlation length varies with quantum dot size

Method accurately captures electron-hole interactions

Size-dependent excitonic properties analyzed

Abstract

The electron-hole correlation length serves as an intrinsic length scale for analyzing excitonic interactions in semiconductor nanoparticles. In this work, the derivation of electron-hole correlation length using the two-particle reduced density is presented. The correlation length was obtained by first calculating the electron-hole cumulant from the pair density,and then transforming the cumulant into intracular coordinates, and finally then imposing exact sum-rule conditions on the radial integral of the cumulant. The excitonic wave function for the calculation was obtained variationally using the electron-hole explicitly correlated Hartree-Fock method. As a consequence, both the pair density and the cumulant were explicit functions of the electron-hole separation distance. The use of explicitly correlated wave function and the integral sum-rule condition are the two key features of this derivation. The method was applied to a series of CdSe quantum dots with diameters 1-20 nm and the effect of dot size on the correlation length was analyzed.