Vertical integration of van der Waals (vdW) materials with atomic precision is an intriguing possibility brought forward by these two-dimensional (2D) materials. Essential to the design and analysis of these structures is a fundamental understanding of the vertical transport of charge carriers into and across vdW materials, yet little has been done in this area. In this report, we explore the important roles of single layer graphene in the vertical tunneling process as a tunneling barrier. Although a semimetal in the lateral lattice plane, graphene together with the vdW gap act as a tunneling barrier that is nearly transparent to the vertically tunneling electrons due to its atomic thickness and the transverse momenta mismatch between the injected electrons and the graphene band structure. This is accentuated using electron tunneling spectroscopy (ETS) showing a lack of features corresponding to the Dirac cone band structure. Meanwhile, the graphene acts as a lateral conductor through which the potential and charge distribution across the tunneling barrier can be tuned. These unique properties make graphene an excellent 2D atomic grid, transparent to charge carriers, and yet can control the carrier flux via the electrical potential. A new model on the quantum capacitance’s effect on vertical tunneling is developed to further elucidate the role of graphene in modulating the tunneling process. This work may serve as a general guideline for the design and analysis of vdW vertical tunneling devices and heterostructures, as well as the study of electron/spin injection through and into vdW materials.

中文翻译：

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石墨烯垂直传输对量子隧穿控制的研究

范德华（vdW）材料与原子精度的垂直集成是这些二维（2D）材料带来的一种令人感兴趣的可能性。对这些结构的设计和分析必不可少的是，对电荷载流子在vdW材料中的垂直传输和穿过vdW材料的垂直传输有基本的了解，但是在这一领域几乎没有做任何事情。在本报告中，我们探讨了单层石墨烯在垂直隧穿过程中作为隧穿势垒的重要作用。尽管半金属在横向晶格平面中，但石墨烯与vdW间隙一起用作隧穿势垒，由于其原子厚度和注入电子与石墨烯能带结构之间的横向力矩失配，该势垒对垂直隧穿电子几乎是透明的。使用电子隧穿光谱法（ETS）强调了这一点，显示出缺乏与狄拉克锥带结构相对应的特征。同时，石墨烯充当横向导体，通过该横向导体可以调节跨越隧穿势垒的电势和电荷分布。这些独特的性能使石墨烯成为出色的2D原子网格，对电荷载流子透明，但仍可以通过电势控制载流子通量。建立了关于量子电容对垂直隧穿的影响的新模型，以进一步阐明石墨烯在调制隧穿过程中的作用。这项工作可作为vdW垂直隧穿器件和异质结构的设计和分析以及研究通过vdW材料和向vdW材料注入电子/自旋的一般指导。