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.

本研究针对由伯纳尔双层石墨烯（Bernal bilayer graphene, BLG）与六方氮化硼（hexagonal boron nitride, hBN）构成的范德瓦尔斯异质结开展了系统性探究。通过第一性原理计算，我们复现了多种堆叠与封装构型下BLG的核心能带结构特征。我们采用包含轨道项与自旋轨道耦合（spin-orbit coupling, SOC）项的低能有效哈密顿模型，重现了hBN修饰后BLG的能带色散、自旋劈裂与自旋期望值。尤为关键的是，hBN层会在BLG的能带谱中打开轨道带隙，其数值可在0至数十毫电子伏特（meV）之间变化，具体取决于原子间的精确堆叠排布。因此，在实验相关的莫尔结构中，可能出现显著的局域带隙差异。此外，SOC参数的数值极小（仅为数至数十微电子伏特，µeV），与未修饰的BLG一致，但会被hBN层通过近邻效应显著调控。当BLG被单层hBN封装时，体系的反演对称性得以恢复，此时能带的轨道带隙与自旋劈裂均会消失。我们还发现，横向电场主要调控石墨烯层间的电势差，在电场强度不超过约1 V/nm时，该电势差与轨道带隙呈现完美的线性相关关系。此外，层分辨拉什巴（Rashba）耦合强度可通过电场以约5 µeV/(V/nm)的速率调控。最后，我们研究了扭转角在6°–20°之间的扭转BLG/hBN异质结构，发现全局能带隙随扭转角线性增大。外推得到的0°扭转角下的带隙约为23 meV，其数值大致等于堆叠依赖的局域带隙的平均值。本研究为hBN/BLG异质结的近邻自旋物理提供了理论见解，可用于解读扩展体系与受限（量子点，quantum dot）体系的相关实验结果。