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arXiv 2103.05869cond-mat.mes-hall
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通过分析和数值计算对半导体中任何拓扑结构的Wannier量子位进行基本描述

Fundamental description of Wannier qubits of any topology in semiconductor by analytical and numerical computations

Krzysztof Pomorski

摘要:

本文从薛定谔理论出发,对基于位置的半导体量子比特的各种拓扑结构的紧束缚模型进行了论证。简单的紧束缚模型允许描述大集成规模的单电子器件。这是由于紧束缚模型忽略了薛定谔模型中由电子-电子相互作用产生的积分-微分方程。给出了从薛定谔方程导出紧束缚模型的两种方法。第一种方法是利用由薛定谔方程得到的格林函数。第二种方法是将泰勒展开应用于薛定谔方程。所得结果可推广到多个Wannier量子比特的情形,并可应用于二维和三维模型。在薛定谔形式下,我们提出了各种关联函数,这些函数可以用来描述Wannier量子比特系统中静态和含时的电场和磁场极化。所提出的工作的中心结果之一依赖于耗散过程的出现在光滑弯曲的半导体纳米线的经典和量子图像的情况下。所给出的结果给出了任何拓扑结构的静电Q交换门的物理描述使用开环纳米线的基础。我们观察到强烈的本地化的波包由于纳米线弯曲。

英文摘要:

Justification of tight-binding model from Schroedinger formalism for various topologies of position-based semiconductor qubits is presented in this work. Simplistic tight-binding model allows for description of single-electron devices at large integration scale. However it is due to the fact that tight-binding model omits the integro-differential equations that arise from electron-electron interaction in Schroedinger model. Two approaches are given in derivation of tight-binding model from Schroedinger equation. First approach is conducted by usage of Green functions obtained from Schroedinger equation. Second approach is given by usage of Taylor expansion applied to Schroedinger equation. The obtained results can be extended for the case of many Wannier qubits with more than one electron and can be applied to 2 and 3 dimensional model. Furthermore various correlation functions are proposed in Schroedinger formalism that can account for static and time-dependent electric and magnetic field polarizing given Wannier qubit system. One of the central results of presented work relies on the emergence of dissipation processes during smooth bending of semiconductor nanowires both in the case of classical and quantum picture. Presented results give the base for physical description of electrostatic Q-Swap gate of any topology using open loop nanowires. We observe strong localization of wavepacket due to nanowire bending.

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