Scattering-matrix method for ballistic electron transport: Theory and an application to quantum antidot arrays.
Scattering-matrix method for ballistic electron transport: Theory and an application to quantum antidot arrays.
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DOI：
10.1103/physrevb.50.8469
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发表时间：
1994-09
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影响因子：
--
通讯作者：
Xu
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文献类型：
--
作者：
Xu
在本文中，我们提出了一个散射矩阵的形式主义来研究电子在介观系统，如具有强调制电位的横向antidot阵列输运。我们表明，物理上重要的和本地化程度较低的状态被允许占主导地位的形式主义的实施，因此，在横向电子输运的转移矩阵方法的应用中经常遇到的数值不稳定性的问题已经得到解决。作为其应用的一个例子，形式主义是用来计算在一个狭窄的二维电子气（2DEG）收缩定义的一维（1D）反点阵列的电子传输。我们发现，当反点的调制电位较弱时，电导带可以出现在窄的2DEG收缩的电导平台的边缘。在强调制的情况下，计算得到的一维反点阵列的电导在高费米能区表现出两种强涨落，即慢涨落和快涨落。慢波动的结果从波的干扰和形成的阵列中的电子minigaps和不敏感的温度高达几个开尔文，而快速波动反映的电子minibands的形成，可以很容易地通过热平均平滑。由于强调制反点阵列中与不同一维路径相关的能带之间存在强烈的重叠，即使在非常低的温度下，也只能在低费米能范围内观察到规则能带形成的影响。
In this paper we present a scattering-matrix formalism to study electron transport in a mesoscopic system such as a lateral antidot array with a strong modulation potential. We show that the physically important and less localized states are allowed to dominate in the implementation of the formalism and, therefore, the problem of the numerical instability that one often encounters in the application of the transfer-matrix method to lateral electron transport has been solved. As an example of its application, the formalism is used to calculate the electron transmission in one-dimensional (1D) antidot arrays defined in a narrow two-dimensional electron-gas (2DEG) constriction. We show that when the modulation potential of antidots is weak the conductance bands can appear at the edges of the conductance plateaus of the narrow 2DEG constriction. In the case of strong modulation the calculated conductance of the 1D antidot arrays are seen to be characterized by two kinds of strong fluctuations, namely, the slow and rapid fluctuations, in high Fermi-energy range. The slow fluctuations result from wave interferences and the formation of the electron minigaps in the arrays and are insensitive to the temperature up to a few Kelvin, while the rapid fluctuations reflect the formation of the electron minibands and can be easily smoothed out by thermal averaging. Due to strong overlaps between the minibands associated with different 1D paths in the strongly modulated antidot arrays, the effects of the regular miniband formation may only be observed in the low Fermi-energy range, even at very low temperature.