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首页> 外文期刊>Physical review >Edge effects in graphene nanostructures: From multiple reflection expansion to density of states
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Edge effects in graphene nanostructures: From multiple reflection expansion to density of states

机译：石墨烯纳米结构的边缘效应：从多重反射扩展到态密度

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摘要

We study the influence of different edge types on the electronic density of states of graphene nanostructures. To this end we develop an exact expansion for the single-particle Green's function of ballistic graphene structures in terms of multiple reflections from the system boundary, which allows for a natural treatment of edge effects. We first apply this formalism to calculate the average density of states of graphene billiards. While the leading term in the corresponding Weyl expansion is proportional to the billiard area, we find that the contribution that usually scales with the total length of the system boundary differs significantly from what one finds in semiconductor-based, Schrodinger-type billiards: The latter term vanishes for armchair and infinite-mass edges and is proportional to the zigzag edge length, highlighting the prominent role of zigzag edges in graphene. We then compute analytical expressions for the density of states oscillations and energy levels within a trajectory-based semiclassical approach. We derive a Dirac version of Gutzwiller's trace formula for classically chaotic graphene billiards and further obtain semiclassical trace formulas for the density of states oscillations in regular graphene cavities. We find that edge-dependent interference of pseudospins in graphene crucially affects the quantum spectrum.
机译：我们研究了不同边缘类型对石墨烯纳米结构态电子密度的影响。为此，我们从系统边界的多次反射角度出发，为弹道石墨烯结构的单粒子格林函数开发了一种精确的扩展，从而可以自然地处理边缘效应。我们首先应用这种形式主义来计算石墨烯台球的平均状态密度。虽然相应的Weyl膨胀中的前导项与台球面积成正比，但我们发现通常随系统边界总长度成比例增加的贡献与基于半导体的Schrodinger型台球所发现的明显不同：后者该术语在扶手椅和无限质量边缘中消失，并且与之字形边缘的长度成比例，突出了之字形边缘在石墨烯中的突出作用。然后，我们在基于轨迹的半经典方法中计算状态振动密度和能级的解析表达式。我们推导了经典混沌石墨烯台球的Gutzwiller跟踪公式的Dirac版本，并进一步获得了规则石墨烯腔中状态振动密度的半经典跟踪公式。我们发现，石墨烯中假纺丝的边缘依赖性干扰对量子光谱有至关重要的影响。

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