Rycerz Adam
Institute for Theoretical Physics, Jagiellonian University, Łojasiewicza 11, PL-30348 Kraków, Poland.
Materials (Basel). 2025 Apr 29;18(9):2036. doi: 10.3390/ma18092036.
The peculiar electronic properties of graphene, including the universal conductivity and the pseudodiffusive shot noise, are usually found in a small vicinity close to the charge neutrality point, away from which the electron's effective mass raises, and nanostructures in graphene start to behave similarly to familiar Sharvin contacts in semiconducting heterostructures. Recently, it was pointed out that as long as abrupt potential steps separate the sample area from the leads, some graphene-specific features can be identified relatively far from the charge neutrality point. These features include greater conductance reduction and shot noise enhancement compared to the standard Sharvin values. The purpose of this paper is twofold: First, we extend the previous analysis based on the effective Dirac equation, and derive the formulas that allow the calculation of the arbitrary charge transfer cumulant for doped graphene. Second, the results of the analytic considerations are compared with numerical simulations of quantum transport on the honeycomb lattice for selected nanosystems for which considerations starting from the Dirac equation cannot be directly adapted. For a wedge-shaped constriction with zigzag edges, the transport characteristics can be tuned from graphene-specific () values to standard Sharvin values by varying the electrostatic potential profile in the narrowest section. A similar scenario is followed by the half-Corbino disk. In contrast, a circular quantum dot with two narrow openings showing a mixed behavior appears: the conductance is close to the Sharvin value, while the Fano factor approaches the value characterizing the symmetric chaotic cavity. Carving a hole in the quantum dot to eliminate direct trajectories between the openings reduces the conductance to sub-Sharvin value, but the Fano factor is unaffected. Our results suggest that experimental attempts to verify the predictions for the sub-Sharvin transport regime should focus on systems with relatively wide openings, where the scattering at the sample edges is insignificant next to the scattering at the sample-lead interfaces.
石墨烯独特的电子特性，包括普遍的导电性和赝扩散散粒噪声，通常在靠近电荷中性点的小范围内出现，远离该点时电子的有效质量增加，并且石墨烯中的纳米结构开始表现得类似于半导体异质结构中常见的沙尔文接触。最近，有人指出，只要陡峭的势垒将样品区域与引线隔开，一些石墨烯特有的特征就能在离电荷中性点相对较远的地方被识别出来。这些特征包括与标准沙尔文值相比更大的电导降低和散粒噪声增强。本文的目的有两个：第一，我们扩展了基于有效狄拉克方程的先前分析，并推导了允许计算掺杂石墨烯任意电荷转移累积量的公式。第二，将解析考虑的结果与选定纳米系统在蜂窝晶格上的量子输运数值模拟进行比较，对于这些纳米系统，从狄拉克方程出发的考虑不能直接适用。对于具有锯齿形边缘的楔形收缩，通过改变最窄部分的静电势分布，可以将输运特性从石墨烯特有的（）值调整到标准沙尔文值。半科贝诺盘也遵循类似的情况。相比之下，具有两个窄开口的圆形量子点表现出混合行为：电导接近沙尔文值，而法诺因子接近表征对称混沌腔的值。在量子点上挖孔以消除开口之间直接的轨迹会将电导降低到亚沙尔文值，但法诺因子不受影响。我们的结果表明，验证亚沙尔文输运 regime 预测的实验尝试应集中在具有相对宽开口的系统上，在这些系统中，样品边缘的散射相对于样品 - 引线界面处的散射可以忽略不计。
