Abstract

Zitterbewegung (jittery motion) of Dirac electrons in single-layer graphene is considered as a nonrelativistic analog of the phenomenon predicted by Erwin Schrödinger for relativistic electrons in free space. It is shown that Dirac electrons in single-layer graphene experience fast fluctuations of their positions around the mean value with fairly a high frequency, which, however, is much lower than for relativistic electrons in free space. The interplay of Zitterbewegung of the wavepackage of conduction electrons formed by the Fermi–Dirac distribution and the low-temperature high-frequency complex conductivity of single-layer graphene has been examined. It is shown that, at low temperatures, the electromagnetic resonance properties of single-layer graphene above the threshold can be simulated using a set of equivalent electric oscillating circuits (oscillators) so that there is always the one that resonates and generates active conductivity. This can be used to visualize electromagnetic processes, which is especially important for including graphene into micro- and nanoelectronic systems. The results obtained can be used, in particular, in the development of a graphene nanoantenna.

中文翻译：

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低温下电子的Zitterbewegung和单层石墨烯的高频电导率

摘要

单层石墨烯中Dirac电子的Zitterbewegung（抖动运动）被认为是ErwinSchrödinger预测的自由空间中相对论电子现象的非相对论模拟。结果表明，单层石墨烯中的狄拉克电子以很高的频率在平均值附近快速发生位置波动，但是，这比自由空间中的相对论电子要低得多。研究了费米-狄拉克分布形成的导电电子波包的Zitterbewegung与单层石墨烯的低温高频复电导率的相互作用。结果表明，在低温下，可以使用一组等效的电振荡电路（振荡器）来模拟阈值以上的单层石墨烯的电磁谐振特性，从而始终存在一个谐振并产生有源电导率的电路。这可用于可视化电磁过程，这对于将石墨烯包含到微电子和纳米电子系统中尤其重要。获得的结果尤其可以用于石墨烯纳米天线的开发中。