電子波導已經被證實能在石墨烯上實現。有團隊曾經利用懸空的石墨烯和電極閘做
出了大概 300 奈米的波導管道 [1]。最近，有團隊實驗上利用奈米碳管做為電極閘而
製造出寛度低至 1 奈米的波導管道 [2]。
然而，此團隊的實驗中只有測量奈米碳管的電導值，這是在電子在石墨烯上有單態
傳輸的一個徵兆，但卻沒有單態傳輸的最直接證據，也就是對石墨烯做傳輸測量。
為了在理論上證明 [2] 裡所提到的主張並且提供一個可靠的指引給日後的實驗，我們
考慮了跟 [2] 一樣的系統來模擬零溫下零雜質的石墨烯的量子傳輸。我們的模擬結果
顯示，透過降低電流注入端和接收端的寬，百分之百的傳輸效率是有可能達到的。
為了更明確的找出完美傳輸的必要條件，我們也給出了在不同的晶格方向、不同的
波導方向、裝置的不同大小、石墨烯的乾淨程度等各種情況下的量子傳輸結果。

Electron waveguide in graphene was previously reported using suspended samples with the guiding channel created by local gates of widths around 300 nm[1]. Very recently, using carbon nanotubes (CNT) as gating for the thinnest possible guiding channel down to 1nm in graphene was ”experimentally proposed” [2].
However, in that report [2], only the signatures of single guided mode in graphene were reported by measuring the conductance of the CNT. No direct transport measurement on graphene was performed. To theoretically confirm the proposal of [2] and provide a reliable guide to future transport experiments, here we consider the geometry of [2] to perform quantum transport simulations in the fully ballistic limit at zero temperature. The results show that by narrowing down the width of the injector and detector, it is possible to achieve 100% of the guiding efficiency.
Further detailed transport simulations have been performed considering various conditions, such as lattice direction, guiding channel orientation, size of the device, disorder scattering, and lead orientation in order to identify the conditions necessary for achieving perfect guiding.

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