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

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.

keywords: explicitly correlated, Gaussian-type geminal, electron-hole correlation, reduced density matrix, cumulant, transition density matrix

References in corpus (3)

• Exact Algorithm for Sampling the 2D Ising Spin Glass
• Variational solution of congruent transformed Hamiltonian for many-electron systems using full configuration interaction calculation
• Development of polaron-transformed explicitly correlated full configuration interaction method for investigation of quantum-confined Stark effect in GaAs quantum dots