论文标题
在六边形硼硼上放松扭曲的双层石墨烯的双Moiré超级晶格中的对称性破裂
Symmetry breaking in the double moiré superlattices of relaxed twisted bilayer graphene on hexagonal boron nitride
论文作者
论文摘要
我们研究了几乎与六边形的硝酸硼（BN）对齐的完全松弛的扭曲双层石墨烯（TBG）中相同双Moiré超晶格的原子和电子结构。考虑到放松效果的单粒子有效的哈密顿（$ \ hat {h}^0 $），而BN引入的完整MoiréHamiltonian已为TBG/BN构建。相对于电荷中立点（CNP），自一成能的Hartree-fock（Schf）接地状态的平均场（MF）带结构是基于$ \ hat {h h}^0 $在平面波式的基础上获得的。 TBG/bn中的单粒子平面频带由于$ \ hat {h}^0 $的对称性破裂而被CNP的打开间隙分开。我们发现，$ \ hat {h}^0 $中的损坏的$ C_2 $对称性主要来自与BN相邻的石墨烯层中的内部反演 - 空气对称结构变形，这引入了内部层次吉尔顿人的空间不均匀的修饰。宽大的扁平乐队具有有限的Chern号码。对于具有魔术角角的TBG/BN，具有$ |ν| $ = 1-3的SCHF接地状态都在狭窄的MF间隙中隔离。当填充平面传导带时，$ν$ = 1的差距小于$ν$ = 3的差距，这表明与平面Chern带相关的非平凡拓扑特性更可能在$ν= 3 $时观察到。这对于带有空价带的负$ν$类似。 TBG/BN对正$ν$的电子结构的依赖性与最近的实验观测大致一致。
We study the atomic and electronic structures of the commensurate double moiré superlattices in fully relaxed twisted bilayer graphene (TBG) nearly aligned with the hexagonal boron nitride (BN). The single-particle effective Hamiltonian ($\hat{H}^0$) taking into account the relaxation effect and the full moiré Hamiltonian introduced by BN has been built for TBG/BN. The mean-field (MF) band structures of the self-consistent Hartree-Fock (SCHF) ground states at different number ($ν$) of filled flat bands relative to the charge neutrality point (CNP) are obtained based on $\hat{H}^0$ in the plane-wave-like basis. The single-particle flat bands in TBG/BN become separated by the opened gap at CNP due to the symmetry breaking in $\hat{H}^0$. We find that the broken $C_2$ symmetry in $\hat{H}^0$ mainly originates from the intralayer inversion-asymmetric structural deformation in the graphene layer adjacent to BN, which introduces spatially non-uniform modifications of the intralayer Hamiltonian. The gapped flat bands have finite Chern numbers. For TBG/BN with the magic twist angle, the SCHF ground states with $|ν|$ = 1-3 are all insulating with narrow MF gaps. When the flat conduction bands are filled, the gap at $ν$ = 1 is smaller than that at $ν$ = 3, suggesting that the nontrivial topological properties associated with the flat Chern bands are more likely to be observed at $ν= 3$. This is similar for negative $ν$ with empty valence bands. The dependence of the electronic structure of TBG/BN on positive $ν$ is roughly consistent with recent experimental observations.
