Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Aleja Mickiewicza 30, 30-059 Kraków, Poland.
J Phys Condens Matter. 2013 Aug 21;25(33):335801. doi: 10.1088/0953-8984/25/33/335801. Epub 2013 Jul 24.
We perform a numerical simulation of the mapping of charge confined in quantum dots by the scanning probe technique. We solve the few-electron Schrödinger equation with the exact diagonalization approach and evaluate the energy maps as a function of the probe position. Next, from the energy maps we try to reproduce the charge density distribution using an integral equation given by the perturbation theory. The reproduced density maps are compared with the original ones. This study covers two-dimensional quantum dots of various geometries and profiles with the one-dimensional (1D) quantum dot as a limiting case. We concentrate on large quantum dots for which strong electron-electron correlations appear. For circular dots the correlations lead to the formation of Wigner molecules that in the presence of a tip appear in the laboratory frame. The unperturbed rotationally-symmetric charge density is surprisingly well reproduced by the mapping. We find in general that the size of the confined droplet as well as the spatial extent of the charge density maxima is underestimated for a repulsive tip potential and overestimated for an attractive tip. In lower symmetry quantum dots Wigner molecules with single-electron islands nucleate for some electron numbers even in the absence of a tip. These charge densities are well resolved by the mapping. These single-electron islands appear in the laboratory frame provided that the classical point charge density distribution is unique, in the 1D limit of confinement in particular. We demonstrate that for electron systems which possess a few equivalent classical configurations the repulsive probe switches between the configurations. In consequence the charge density evades mapping by the repulsive probe.
我们对通过扫描探针技术限制在量子点中的电荷的映射进行了数值模拟。我们用精确对角化方法求解了少电子薛定谔方程，并将能量图作为探针位置的函数进行了评估。接下来，我们从能量图中尝试使用由微扰理论给出的积分方程来重现电荷密度分布。将重现的密度图与原始密度图进行比较。本研究涵盖了具有一维（1D）量子点极限情况的各种几何形状和轮廓的二维量子点。我们集中研究了出现强电子-电子相关的大量子点。对于圆形点，相关性导致威格纳分子的形成，在存在尖端的情况下，威格纳分子出现在实验室框架中。令人惊讶的是，未受扰的旋转对称电荷密度通过映射得到了很好的重现。我们发现，一般来说，对于排斥尖端势，受限液滴的大小以及电荷密度最大值的空间延伸被低估，而对于吸引尖端则被高估。在较低对称性的量子点中，即使没有尖端，对于某些电子数，也会形成具有单电子岛的威格纳分子。这些电荷密度可以通过映射很好地分辨。这些单电子岛出现在实验室框架中，前提是经典点电荷密度分布是唯一的，特别是在限制为 1D 的极限情况下。我们证明，对于具有几个等效经典构型的电子系统，排斥探针在构型之间切换。因此，排斥探针使电荷密度逃避映射。
