Department of Physics and Astronomy, Rice University, P.O. Box 1892, Houston, Texas 77251, USA.
J Chem Phys. 2011 Sep 28;135(12):124704. doi: 10.1063/1.3640889.
We report on the theoretical investigation of the elementary electronic excitations in a quantum wire made up of vertically stacked self-assembled InAs/GaAs quantum dots. The length scales (of a few nanometers) involved in the experimental setups prompt us to consider an infinitely periodic system of two-dimensionally confined (InAs) quantum dot layers separated by GaAs spacers. The resultant quantum wire is characterized by a two-dimensional harmonic confining potential in the x-y plane and a periodic (Kronig-Penney) potential along the z (or the growth) direction within the tight-binding approximation. Since the wells and barriers are formed from two different materials, we employ the Bastard's boundary conditions in order to determine the eigenfunctions along the z direction. These wave functions are then used to generate the Wannier functions, which, in turn, constitute the legitimate Bloch functions that govern the electron dynamics along the direction of periodicity. Thus, the Bloch functions and the Hermite functions together characterize the whole system. We then make use of the Bohm-Pines' (full) random-phase approximation in order to derive a general nonlocal, dynamic dielectric function. Thus, developed theoretical framework is then specified to work within a (lowest miniband and) two-subband model that enables us to scrutinize the single-particle as well as collective responses of the system. We compute and discuss the behavior of the eigenfunctions, band-widths, density of states, Fermi energy, single-particle and collective excitations, and finally size up the importance of studying the inverse dielectric function in relation with the quantum transport phenomena. It is remarkable to notice how the variation in the barrier- and well-widths can allow us to tailor the excitation spectrum in the desired energy range. Given the advantage of the vertically stacked quantum dots over the planar ones and the foreseen applications in the single-electron devices and in the quantum computation, it is quite interesting and important to explore the electronic, optical, and transport phenomena in such systems.
我们报告了在由垂直堆叠的自组装 InAs/GaAs 量子点组成的量子线中基本电子激发的理论研究。实验设置所涉及的长度尺度（为数纳米）促使我们考虑二维受限（InAs）量子点层的无限周期系统，这些量子点层由 GaAs 间隔物隔开。所得的量子线在 x-y 平面内具有二维调和限制势，在紧束缚近似下沿 z（或生长）方向具有周期性（Kronig-Penney）势。由于阱和势垒由两种不同的材料形成，我们采用 Bastard 的边界条件来确定 z 方向的本征函数。这些波函数随后用于生成 Wannier 函数，它们反过来构成控制沿周期性方向电子动力学的合法 Bloch 函数。因此，Bloch 函数和 Hermite 函数共同描述了整个系统。然后，我们利用 Bohm-Pines（全）随机相位近似来推导出一般的非局部、动态介电函数。因此，开发的理论框架指定在（最低的最小能带和）双子带模型内工作，这使我们能够仔细研究系统的单粒子和集体响应。我们计算和讨论了本征函数、带宽、态密度、费米能、单粒子和集体激发的行为，并最终评估了研究与量子输运现象相关的逆介电函数的重要性。值得注意的是，势垒和阱宽度的变化如何使我们能够在所需的能量范围内调整激发谱。鉴于垂直堆叠量子点相对于平面量子点的优势以及在单电子器件和量子计算中的预期应用，探索此类系统中的电子、光学和输运现象是非常有趣和重要的。
