Resonating UHF Study on Electron Correlation in a Ground State of Two Electrons Confined in 2D Quantum Dot
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Resonating UHF Study on Electron Correlation in a Ground State of Two Electrons Confined in 2D Quantum Dot Takuma Okunishi and Kyozaburo Takeda Department of Electrical Engineering and Bioscience, Waseda University, Tokyo 169-8555, Japan ABSTRACT We theoretically study the spatial and temporal fluctuation of two electrons confined in a semiconductor quantum dot (QD). Eigenstates are determined by the resonating unrestricted Hartree-Fock (res-UHF) approach in order to take into account the electron correlation via the configuration interaction (CI). The time-dependent (TD) wave function is, then, expanded by the UHF solutions, and the CI treatment is combined with the TD Schrödinger equation (TD-CI). The present TD-CI approach has an advantage to study how the electron correlation fluctuates the multi-electron state spatially and/or temporally through the multi-reference description of many-electron wave functions. INTRODUCTION In nano-meter sized QDs, a long-range Coulomb force overcomes the confinement potential and causes many curious and interesting phenomena due to the electron correlation. Many theories and computational studies have been carried out to reveal the role of electron correlation and relating electronic properties [1-5]. Accordingly we have considerably deepened our understanding of the static electronic states for various shaped QDs. However, less study has been achieved for the TD phenomena of strongly correlated multi-electron systems. Here, we study the TD spatial fluctuation about one of the multi-electron systems by combining with the res-UHF approach [6-7]. Considering that electrons in most of experiments are initially in noneigenstate of the system, it is remarkably important to understand the TD phenomena in any systems. We here study this subject via two electrons confined in a square QD with the spin singlet multiplicity (S=1). THEORY The UHF approach gives several scf-solutions for two electrons confined in a square QD with S=1 (figure 1). However those solutions break the symmetry nature due to the lack of the electron correlation when the confinement length elongates. Those OA and OS (see figure 1) do not have the C4 axis symmetry, and the resulting UHF solutions are no longer the irreducible representations of the present Hamiltonian having point group symmetry of D4h. In order to include the correlation effect precisely, we employ the res-UHF CI method, and represent many-electron eigenstates through the multi-reference description of the full wave function. This method is simple but intuitive to approximate a many-body wave function by the superposition of nonorthogonal Slater determinants (SDs). The UHF scf-solutions of OA, OS and IT, indicated in figure 1, are employed with taking into account the Heitler-London (HL) configuration because of S=1. Although these UHF solutions are not orthogonal, this small
number of bases is advantageous for narrowing down the number of employed SDs [8]. The calculational accuracy depends on the choice of the SDs sets. In order to demonstrate t
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