Non-identical moire twins in bilayer graphene revealed by valley Hall effect measurements

The superlattice obtained by aligning a monolayer graphene and boron nitride (BN) inherits from the hexagonal lattice a sixty degrees periodicity with the layer alignment. It implies that, in principle, the properties of the heterostructure must be identical for 0$^{\circ}$ and 60$^{\circ}$ of layer alignment. Here, we demonstrate, using dynamically rotatable van der Waals heterostructures, that the moir\'e superlattice formed in a bilayer graphene/BN has different electronic properties at 0$^{\circ}$ and 60$^{\circ}$ of alignment. Although the existence of these non-identical moir\'e twins is explained by different relaxation of the atomic structures for each alignment, the origin of the observed valley Hall effect remains to be explained. A simple Berry curvature argument do not hold to explain the hundred and twenty degrees periodicity of this observation. Our results highlight the complexity of the interplay between mechanical and electronic properties on moir\'e structure and the importance of taking into account atomic structure relaxation to understand its electronic properties.将单层石墨烯与氮化硼（BN）对齐后得到的超晶格，继承了六角晶格与层对齐相关的60°周期性。这意味着，原则上该异质结构的特性在层对齐角度为0°与60°时应当完全一致。本文中，我们借助可动态旋转的范德华异质结构（van der Waals heterostructures），证明了双层石墨烯/BN形成的莫尔超晶格（moiré superlattice）在0°与60°对齐时，其电子特性存在差异。尽管这类莫尔孪晶的非等价性可通过两种对齐方式下原子结构的不同弛豫过程予以解释，但所观测到的谷霍尔效应（valley Hall effect）的起源仍有待阐明。仅依靠简单的贝里曲率（Berry curvature）理论无法解释该观测结果所呈现的120°周期性。我们的研究结果凸显了莫尔结构中力学与电子特性相互作用的复杂性，以及考虑原子结构弛豫对理解其电子特性的重要性。