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arXiv 1104.5491cond-mat.mes-hallquant-ph
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半导体双量子点系统电荷稳定图的量子理论

Quantum theory of the charge stability diagram of semiconductor double quantum dot systems

Xin Wang, Shuo Yang, S. Das Sarma

摘要:

我们完成了我们最近介绍的理论框架处理双量子点系统的推广形式的哈伯德模型。详细讨论了模型中所有量子参数对电荷稳定图的影响。的微观理论的一般配方,并截断在一个轨道每个网站,我们研究的影响不同的选择模型的禁闭势的哈伯德参数以及电荷稳定性图。我们计算了保持每个位置三个轨道的电荷稳定性图,发现附加的高躺轨道对仅具有最低能量轨道的子空间的影响可以被视为Hubbard参数的小重整化,从而证明了我们在所有其他计算中只保持最低轨道的做法是合理的。谐振子频率在高斯模型势的实施中的作用进行了讨论,并确定了外部磁场的效果类似于选择一个更本地化的电子波函数在微观计算。在附录中给出了包括所有可能的交换项在内的哈密顿量的完整矩阵形式,以及由于非物理参数而引起的几个特殊的电荷稳定性图,从而强调了在获得定义哈密顿量的系统参数时可靠的微观模型的至关重要性。

英文摘要:

We complete our recently introduced theoretical framework treating the double quantum dot system with a generalized form of Hubbard model. The effects of all quantum parameters involved in our model on the charge stability diagram are discussed in detail. A general formulation of the microscopic theory is presented, and truncating at one orbital per site, we study the implication of different choices of the model confinement potential on the Hubbard parameters as well as the charge stability diagram. We calculate the charge stability diagram keeping three orbitals per site and find that the effect of additional higher-lying orbitals on the subspace with lowest-energy orbitals only can be regarded as a small renormalization of Hubbard parameters, thereby justifying our practice of keeping only the lowest-orbital in all other calculations. The role of the harmonic oscillator frequency in the implementation of the Gaussian model potential is discussed, and the effect of an external magnetic field is identified to be similar to choosing a more localized electron wave function in microscopic calculations. The full matrix form of the Hamiltonian including all possible exchange terms, and several peculiar charge stability diagrams due to unphysical parameters are presented in the appendix, thus emphasizing the critical importance of a reliable microscopic model in obtaining the system parameters defining the Hamiltonian.

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