Gapped graphene has been proposed to be a good platform to observe the valley Hall effect, a transport phenomenon involving the flow of electrons that are characterized by different valley indices. In the present work, we show that this phenomenon is better described as an instance of the orbital Hall effect (OHE), where the ambiguous “valley” indices are replaced by a physical quantity, the orbital magnetic moment, which can be defined uniformly over the entire Brillouin zone. This description removes the arbitrariness in the choice of arbitrary cutoff for the valley-restricted integrals in the valley Hall conductivity, as the conductivity in the OHE is now defined as the Brillouin zone integral of a new quantity, called the orbital Berry curvature. This reformulation in terms of OHE provides a direct explanation to the accumulated opposite orbital moments at the edges of the sample, observed in previous Kerr rotation measurements.

中文翻译：

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间隙霍尔效应中的霍尔效应可替代谷底霍尔效应

已提出有间隙的石墨烯是观察谷霍尔效应的良好平台，谷霍尔效应是一种传输现象，涉及以不同谷指数为特征的电子流。在目前的工作中，我们表明，这种现象可以更好地描述为轨道霍尔效应（OHE）的一个实例，其中模棱两可的“谷”指数被物理量（轨道磁矩）代替，该物理量可以在整个轨道上统一定义。整个布里渊区。由于OHE中的电导率现在定义为新量的布里渊区积分，称为轨道贝里曲率，因此该描述消除了为谷底霍尔电导率中的谷底限制积分选择任意截止的任意性。