Calculation of the electronic energy eigenvalues and eigenstates and Coulomb and dipole matrix elements for realistically modelled quantum dots

计算真实建模量子点的电子能量本征值和本征态以及库仑和偶极矩阵元素

• 批准号: 5403268
• 负责人: Professor Dr. Gerd Czycholl
• 金额: --
• 依托单位: Institut für Theoretische Physik (ITP)
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2003
• 资助国家: 德国
• 起止时间: 2002-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5403268?language=en
• 关键词: Calculation; electronic; energy; eigenvalues; eigenstates

Using the information on the structure and the composition of the actual quantum dots from the experimental projects I-2, II-1 the electronic properties, i.e. the one-particle eigenenergies and the eigenstates shall be determined starting either from an effective confinement potential characterizing the QD or from a more microscopic tight-binding description of the QD. From the eigenstates one can calculate all one-particle and two-particle matrix elements, in particular the dipole matrix elements, which are important for the selection rules and thus for a calculation of the optical properties, and the Coulomb matrix elements. This leads to an effective Hamiltonian in second quantization with parameters determined for the actual QD. For a small number of electrons per QD this Hamiltonian can be solved exactly, otherwise an appropriate many-body approximation has to be applied to determine the relevant electronic properties including many-body effects.

使用来自实验项目I-2、II-1的关于实际量子点的结构和组成的信息，电子性质，即单粒子本征能量和本征态，将从表征QD的有效约束势或从QD的更微观的紧束缚描述开始确定。从本征态，可以计算所有的单粒子和双粒子矩阵元，特别是偶极矩阵元，这是重要的选择规则，从而计算的光学性质，和库仑矩阵元。这导致了一个有效的哈密顿量在第二量子化的参数确定的实际量子点。对于每个量子点的少量电子，这个哈密顿量可以精确地求解，否则必须应用适当的多体近似来确定包括多体效应在内的相关电子性质。