随机钉扎鼓的本征频率与石墨烯的电导率
Eigenfrequencies of the randomly pinned drum and conductivity of graphene
摘要：
石墨烯是纳米机械应用的方便材料，因为高频振荡很容易获得。在这篇文章中，我们考虑石墨烯在粗糙的基板上附着在随机位置的缺陷。我们探讨了对石墨烯导电性影响最大的低阶声子模的统计特性。我们发现，最近邻间距的低本征频率的Wigner-Dyson概率分布平均后的随机配置的无序。由于电子与膜振荡的相互作用，电子可以转移到更高或更低的能量，这是声子辅助的Tien-Gordon效应的表现。Tien-Gordon效应抑制了石墨烯的导电性。在低费米能级和小尺寸的样品的制度下，观察到电导率的增加，我们指的是克莱因隧穿和电子-空穴对的产生。最终，当透射率的增加变得太显著时，对的产生改变了系统的基态，这表明本文中使用的单粒子狄拉克方程的适用性是有限的。
英文摘要：
Graphene is convenient material for nanomechanichal applications since high-frequency oscillations are easily accessible. In this Article, we consider graphene on a rough substrate attached to imperfections at random locations. We explore the statistics of low-lying phonon modes, which exert most influence on the conductivity of graphene. We find that the nearest neighbor spacings of low lying eigenfrequencies have the Wigner-Dyson probability distribution after averaging over the random configurations of disorder. Due to interaction of electrons with the oscillations of the membrane, an electron can be transfered to higher or lower energies, which is a manifestation of the phonon-assisted Tien-Gordon effect. The Tien-Gordon effect suppresses the conductivity of graphene. In the regime of low Fermi energies and small sizes of the sample an increase of conductivity is observed which we refer to Klein tunneling and electron-hole pair creation. Eventually, when the increase of the transmission becomes too prominent, the pair creation changes the ground state of the system, signalizing the limit of applicability of the single-particle Dirac equation used in this paper.
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