Ballicchia Mauro, Etl Clemens, Nedjalkov Mihail, Weinbub Josef
Institute for Microelectronics, TU Wien, Gusshausstrasse 27-29, 1040 Wien, Austria.
Nanoscale. 2024 Jun 6;16(22):10819-10826. doi: 10.1039/d3nr05796h.
Controlling single-electron states becomes increasingly important due to the wide-ranging advances in electron quantum optics. Single-electron control enables coherent manipulation of individual electrons and the ability to exploit the wave nature of electrons, which offers various opportunities for quantum information processing, sensing, and metrology. Here we explore non-uniform magnetic fields, which offer unique mechanisms for single-electron control. Considering the modeling perspective, conventional electron quantum transport theories are commonly based on gauge-dependent electromagnetic potentials. A direct formulation in terms of intuitive electromagnetic fields is thus not possible. In an effort to rectify this, a gauge-invariant formulation of the Wigner equation for general electromagnetic fields has been proposed [M. Nedjalkov , , 2019, , 014423]. However, the complexity of this equation requires the derivation of a more convenient formulation for linear electromagnetic fields [M. Nedjalkov , , 2022, , 052213]. This formulation directly includes the classical formulation of the Lorentz force and higher-order terms, depending on the magnetic field gradient, that are negligible for small variations of the magnetic field. In this work, we generalize this equation in order to include a general, non-uniform electric field and a linear, non-uniform magnetic field. The thus obtained formulation has been applied to investigate the capabilities of a linear, non-uniform magnetic field to control single-electron states in terms of trajectory, interference patterns, and dispersion. This has led to the exploration of a new type of transport inside electronic waveguides based on snake trajectories and the possibility of splitting wavepackets to realize edge states.
由于电子量子光学领域的广泛进展，控制单电子态变得越来越重要。单电子控制能够对单个电子进行相干操纵，并利用电子的波动特性，这为量子信息处理、传感和计量学提供了各种机会。在这里，我们探索非均匀磁场，它为单电子控制提供了独特的机制。从建模的角度来看，传统的电子量子输运理论通常基于规范依赖的电磁势。因此，不可能直接用直观的电磁场来表述。为了纠正这一点，有人提出了一种适用于一般电磁场的维格纳方程的规范不变表述[M. Nedjalkov, , 2019, , 014423]。然而，这个方程的复杂性要求为线性电磁场推导一个更方便的表述[M. Nedjalkov, , 2022, , 052213]。这个表述直接包含了洛伦兹力的经典表述以及取决于磁场梯度的高阶项，对于磁场的小变化来说这些高阶项可以忽略不计。在这项工作中，我们对这个方程进行了推广，以纳入一般的非均匀电场和线性的非均匀磁场。由此得到的表述已被用于研究线性非均匀磁场在控制单电子态方面的能力，包括轨迹、干涉图样和色散。这导致了对基于蛇形轨迹的电子波导内新型输运的探索，以及分裂波包以实现边缘态的可能性。
