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首页> 外文期刊>The European physical journal, D. Atomic, molecular, and optical physics >Electronic structures in coupled two quantum dots by 3D-mesh Hartree-Fock-Kohn-Sham calculation
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Electronic structures in coupled two quantum dots by 3D-mesh Hartree-Fock-Kohn-Sham calculation

机译：通过3D网格Hartree-Fock-Kohn-Sham计算耦合两个量子点中的电子结构

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摘要

To study the electronic structures of quantum dots in the framework of self-interaction-free including three dimensional effects, we adopt the theory of nonlocal effective potential introduced by Kohn and Sham [1]. For utilizing the advantageous point of the real space (3D) mesh method to solve the original nonlinear and nonlocal Hartree-Fock-Kohn-Sham (HFKS)-equation, we introduce a linearization of the equation in the local form by introducing the local Coulomb potentials which depend on explicitly the two single particle states. In partice, for solving the local form HFKS-equation, we use the Car-Parrinello-like relaxation method and the Coulomb potentials are obtained by solving the Poisson equation under proper boundary conditions. Firstly the observed energy gap between triplet- and singlet-states of N = 4 in DBS [7] is discussed to reproduce the addition energies and chemical potentials depending the magnetic field. Next the coupling between two-quantum dots in TBS [8] is studied by adding the square barrier between two dots. The spin-degeneracy [8] measured in gate-voltage depending on magnetic field is well reproduced in the limit of small mismatch. Finally, the electronic states in the ring structure are calculated and discussed how the ring size and magnetic field affect to the structures.
机译：为了研究包括三维效应在内的无自相互作用的量子点的电子结构，我们采用了Kohn和Sham [1]提出的非局部有效势理论。为了利用实空间（3D）网格方法的优势来求解原始的非线性和非局部Hartree-Fock-Kohn-Sham（HFKS）方程，我们通过引入局部库仑，将方程线性化为局部形式势明显取决于两个单个粒子状态。特别地，为了求解局部形式的HFKS方程，我们使用了类似于Car-Parrinello的松弛方法，并且通过在适当的边界条件下求解Poisson方程来获得库仑势。首先讨论了在DBS [7]中观察到的N = 4的三重态和单重态之间的能隙，以重现依赖于磁场的加能和化学势。接下来，通过在两个点之间添加方形势垒来研究TBS [8]中两个量子点之间的耦合。在栅极电压中根据磁场测量的自旋简并性[8]在很小的失配极限内得到了很好的再现。最后，计算了环形结构中的电子状态，并讨论了环形尺寸和磁场如何影响结构。

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