Zitterbewegung of Electrons and High-Frequency Conductivity of Single-Layer Graphene at Low Temperatures

Abstract

Zitterbewegung (jittery motion) of Dirac electrons in single-layer graphene is considered as a nonrelativistic analog of the phenomenon predicted by Erwin Schrodinger 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.