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.

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

References in corpus (18)

• Collective Transport in Arrays of Quantum Dots
• Structure of Fermionic Density Matrices: Complete N-representability Conditions
• The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
• Magnetic field effects on quantum ring excitons
• Ultracold atoms confined in an optical lattice plus parabolic potential: a closed-form approach
• Controlling the Dynamics of Many-Electron Systems from First Principles: A Marriage of Optimal Control and Time-Dependent Density-Functional Theory
• Singlet-triplet splitting, correlation and entanglement of two electrons in quantum dot molecules
• Diagrammatic Quantum Monte Carlo for Two-Body Problem: Exciton
• Exact Algorithm for Sampling the 2D Ising Spin Glass
• Semiclassical Electron Correlation in Density-Matrix Time-Propagation
• Optical response of small closed-shell sodium clusters
• Collective charge-density excitations of non-circular quantum dots in a magnetic field
• Quantum particle in a parabolic lattice in the presence of a gauge field
• Variational solution of congruent transformed Hamiltonian for many-electron systems using full configuration interaction calculation
• Correlation energy of anisotropic quantum dots
• Electron Correlation via Frozen Gaussian Dynamics
• Development of polaron-transformed explicitly correlated full configuration interaction method for investigation of quantum-confined Stark effect in GaAs quantum dots
• Infinite-order diagrammatic summation approach to explicitly correlated congruent transformed Hamiltonian