论文标题
放松扭曲的三层石墨烯的局部电子结构中的能量稳定性和空间不均匀性
Energetic stability and spatial inhomogeneity in the local electronic structure of relaxed twisted trilayer graphene
论文作者
论文摘要
我们研究了一般扭曲的三层石墨烯（TTG）的能量稳定性和局部电子结构，顶层和底层分别相对于中层旋转了$θ$和$θ'$。在$ 1^{\ circ} \ sim 2^{\ circ} $内，具有$θ$的Moiré-Moiré超级晶格的大约超级电池是$θ^{\ prime} $，以描述带有周期性边界条件的放松TTG的结构和电子属性。完全放松表明，与$θ=θ^{\ prime} $相称的TTG具有固定$θ$的局部最低总能量（$ e_ {tol} $），而$ e_ {tol} $ first to local toper to local Mivires，开始下降，并开始下降，并随着$θ^{\ prime prime的减少而下降。一些区域在顶层和底层显示出增强的平面内放松，但在中层抑制了松弛，并形成了一个具有Moiré-Moiré长度尺度的六边形网络。 The stacking configurations with the atoms in the three layers vertically aligned at the origin of the relaxed TTG supercells at $θ$ around $1.6^{\circ}$ and $θ^{\prime}$ around $1.4^{\circ}$ have a high density of states (DOS) near the Fermi level ($E_F$), which can reach that of the mirror symmetric TTG以大约1.7^{\ circ} $的同等扭曲角度。相比之下，其他一些堆栈可能在$ e_f $左右的dos较低。 DOS对某些TTG超级电池的显着堆叠依赖性表明，当扭曲角略微远离不同堆栈中DOS较大的小型超级电池时，TTG的局部电子结构可以表现出强的空间不均匀性。此外，TTG的结构放松在高DOS及其强大的堆叠依赖性中起着至关重要的作用。
We study the energetic stability and the local electronic structure of the general twisted trilayer graphene (TTG) with the top and bottom layers rotated with respect to the middle layer respectively by $θ$ and $θ'$. Approximate supercells of the moiré-of-moiré superlattices with $θ$ and $θ^{\prime}$ within $1^{\circ}\sim 2^{\circ}$ are established to describe the structural and electronic properties of relaxed TTG with the periodic boundary condition. Full relaxation demonstrates that the commensurate TTG with $θ=θ^{\prime}$ has the local minimum total energy ($E_{tol}$) at a fixed $θ$, while $E_{tol}$ first reaches a local maximum and begins to drop with decreasing $θ^{\prime}$ for $θ^{\prime} < θ$. Some regions exhibit enhanced in-plane relaxation in the top and bottom layers but suppressed relaxation in the middle layer and form a hexagonal network with the moiré-of-moiré length scale. The stacking configurations with the atoms in the three layers vertically aligned at the origin of the relaxed TTG supercells at $θ$ around $1.6^{\circ}$ and $θ^{\prime}$ around $1.4^{\circ}$ have a high density of states (DOS) near the Fermi level ($E_F$), which can reach that of the mirror symmetric TTG with equal twist angles of about $1.7^{\circ}$. In contrast, some other stackings can have rather low DOS around $E_F$. The significant stacking dependence of DOS for some TTG supercells demonstrates that the local electronic structure of TTG can exhibit strong spatial inhomogeneity when the twist angles are slightly away from those of the small supercells with large variations of DOS among different stackings. Moreover, the structural relaxation of TTG plays a crucial role in the high DOS and its strong stacking dependence.
