Electron surface states in solids are typically confined to the outermost atomic layers and, due to surface disorder, have negligible impact on electronic transport. Here, we demonstrate a very different behavior for surface states in graphene. We probe the wavelike character of these states by Fabry–Perot (FP) interferometry and find that, in contrast to theoretical predictions, these states can propagate ballistically over micron-scale distances. This is achieved by embedding a graphene resonator formed by gate-defined p–n junctions within a graphene superconductor–normal–superconductor structure. By combining superconducting Aharanov–Bohm interferometry with Fourier methods, we visualize spatially resolved current flow and image FP resonances due to p–n–p cavity modes. The coherence of the standing-wave edge states is revealed by observing a new family of FP resonances, which coexist with the bulk resonances. The edge resonances have periodicity distinct from that of the bulk states manifest in a repeated spatial redistribution of current on and off the FP resonances. This behavior is accompanied by a modulation of the multiple Andreev reflection amplitude on-and-off resonance, indicating that electrons propagate ballistically in a fully coherent fashion. These results, which were not anticipated by theory, provide a practical route to developing electron analog of optical FP resonators at the graphene edge.

中文翻译：

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石墨烯边缘电子相干和法布里-珀罗驻波的观察

固体中的电子表面态通常被限制在最外层的原子层，并且由于表面紊乱，对电子传输的影响可忽略不计。在这里，我们展示了石墨烯中表面状态的非常不同的行为。我们通过法布里-珀罗（FP）干涉仪研究了这些状态的波状特征，发现与理论预测相反，这些状态可以在微米级距离上进行弹道传播。这是通过将由栅极定义的p–n结形成的石墨烯谐振器嵌入到石墨烯超导体－正常－超导体结构中来实现的。通过将超导Aharanov-Bohm干涉测量与傅立叶方法相结合，我们可以观察到由于p–n–p腔模引起的空间分辨电流和图像FP共振。通过观察与本体共振共存的新的FP共振家族，揭示了驻波边缘状态的相干性。边缘共振的周期性不同于本体态的周期性，这表现为在FP共振上和在FP共振附近电流的重复空间重新分布。此行为伴随着多个Andreev反射振幅的开关共振的调制，表明电子以完全相干的方式弹道传播。这些结果是理论上没有预料到的，为开发在石墨烯边缘的光学FP谐振器的电子类似物提供了实用的途径。边缘共振的周期性不同于本体态的周期性，这表现为在FP共振上和在FP共振附近电流的重复空间重新分布。此行为伴随着多个Andreev反射振幅的开关共振的调制，表明电子以完全相干的方式弹道传播。这些结果是理论上没有预料到的，为开发在石墨烯边缘的光学FP谐振器的电子类似物提供了实用的途径。边缘共振的周期性不同于本体态的周期性，这表现为在FP共振上和在FP共振附近电流的重复空间重新分布。此行为伴随着多个Andreev反射振幅的开关共振的调制，表明电子以完全相干的方式弹道传播。这些结果是理论上没有预料到的，为开发在石墨烯边缘的光学FP谐振器的电子类似物提供了实用的途径。