Department of Physics, Harvard University , 17 Oxford Street, Cambridge, Massachusetts 02138, United States.
Department of Physics, Massachusetts Institute of Technology , 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States.
Nano Lett. 2017 Dec 13;17(12):7380-7386. doi: 10.1021/acs.nanolett.7b03156. Epub 2017 Nov 8.
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.
固态中的电子表面态通常局限于最外层的原子层，并且由于表面无序，对电子输运的影响可以忽略不计。在这里，我们展示了石墨烯中表面态的一种非常不同的行为。我们通过法布里-珀罗（FP）干涉仪探测这些态的波动特性，发现与理论预测相反，这些态可以在微米级距离上弹道传播。这是通过在石墨烯超导-正常-超导结构中嵌入由栅极定义的 p-n 结形成的石墨烯谐振器来实现的。通过将超导 Aharanov-Bohm 干涉仪与傅里叶方法相结合，我们可视化了空间分辨的电流流动，并由于 p-n-p 腔模式而成像 FP 共振。由于观察到新的 FP 共振家族，与体共振共存，边缘驻波态的相干性得以揭示。这些共振的周期性与体状态不同，这表现为在 FP 共振上和下电流的重复空间再分布。这种行为伴随着在共振和非共振上的多重安德烈夫反射幅度的调制，表明电子以完全相干的方式弹道传播。这些结果与理论预期不符，为在石墨烯边缘开发电子光学 FP 谐振器提供了一种实用途径。
