Data archive of Electronic and spin-orbit properties of h-BN encapsulated bilayer graphene

Van der Waals heterostructures consisting of Bernal bilayer graphene (BLG) and hexagonal boron nitride (hBN) are investigated. By performing first-principles calculations, we capture the essential BLG band structure features for several stacking and encapsulation scenarios. A low-energy model Hamiltonian, comprising orbital and spin-orbit coupling (SOC) terms, is employed to reproduce the hBN-modified BLG dispersion, spin splittings, and spin expectation values. Most important, the hBN layers open an orbital gap in the BLG spectrum, which can range from zero to tens of meV, depending on the precise stacking arrangement of the individual atoms. Therefore, large local band gap variations may arise in experimentally relevant moiré structures. Moreover, the SOC parameters are small (few to tens of µeV), just as in bare BLG, but are markedly proximity modified by the hBN layers. Especially when BLG is encapsulated by monolayers of hBN, such that inversion symmetry is restored, the orbital gap and spin splittings of the bands vanish. In addition, we show that a transverse electric field mainly modifies the potential difference between the graphene layers, which perfectly correlates with the orbital gap for fields up to about 1 V/nm. Moreover, the layer-resolved Rashba couplings are tunable by ∼5µeVperV/nm. Finally, by investigating twisted BLG/hBN structures, with twist angles between 6∘–20∘, we find that the global band gap increases linearly with the twist angle. The extrapolated 0∘ band gap is about 23 meV and results roughly from the average of the stacking-dependent local band gaps. Our investigations give insights into proximity spin physics of hBN/BLG heterostructures, which should be useful for interpreting experiments on extended as well as confined (quantum dot) systems.

本研究针对由伯内尔双层石墨烯（BLG）和六方氮化硼（hBN）构成的范德华异质结构进行了探讨。通过进行第一性原理计算，我们捕捉了BLG在不同堆叠和封装情形下的基本能带结构特征。采用包含轨道和自旋轨道耦合（SOC）项的低能模型哈密顿量，以再现hBN修饰后的BLG能带散布、自旋分裂和自旋期望值。尤为重要的是，hBN层在BLG谱中打开了轨道隙，其大小可从零延伸至数十毫电子伏特，取决于单个原子的精确堆叠排列。因此，在实验相关的莫尔结构中可能出现大的局部能带隙变化。此外，SOC参数较小（几至数十微电子伏特），与裸BLG类似，但由hBN层显著邻近修正。特别是当BLG被hBN单层封装，从而恢复反演对称性时，能带的轨道隙和自旋分裂消失。此外，我们还表明，横向电场主要改变石墨烯层间的电势差，这与横向电场高达约1 V/nm时的轨道隙完美相关。此外，通过约5µeV/每V/nm的调节，层分辨的拉什巴耦合是可调的。最后，通过研究扭转BLG/hBN结构，扭转角介于6°至20°之间，我们发现全局能带隙随扭转角的增加呈线性增长。外推的0°能带隙约为23毫电子伏特，大致由堆叠依赖的局部能带隙的平均值所决定。我们的研究为理解hBN/BLG异质结构的邻近自旋物理提供了洞见，这对于解释扩展以及限定（量子点）系统上的实验应有所帮助。