Modeling mechanical relaxation in incommensurate trilayer van der Waals heterostructures
Modeling mechanical relaxation in incommensurate trilayer van der Waals heterostructures
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DOI：
10.1103/physrevb.101.224107
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发表时间：
2019-11
影响因子：
3.7
通讯作者：
Ziyan Zhu;Paul Cazeaux;M. Luskin;E. Kaxiras
中科院分区：
文献类型：
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作者：
Ziyan Zhu;Paul Cazeaux;M. Luskin;E. Kaxiras
从理论上讲，多层二维材料的无公度堆积是一个具有挑战性的问题，也是操纵其物理性质的一个有趣的途径。在这里，我们提出了一个多尺度模型来获得具有两个独立扭角的扭曲三层范德华(VDW)异质结的力学弛豫图案，这是一个通常没有超晶胞描述的无公度系统。我们采用组态空间作为这种无公度层状材料的自然描述，基于原子位置的局域环境，绕过了公度近似的需要。为了得到松弛模式，我们对松弛位移矢量进行能量最小化。我们用一个连续介质模型结合广义层错能来描述层间耦合，这是基于密度泛函理论的第一性原理计算得到的。我们发现扭曲的三层石墨烯和{WSe_2}是由于两个双层莫尔图案的无公度耦合而产生的“莫尔云纹”。我们还发现，与扭曲双层膜中保持对称性的面内驰豫相比，当两个扭转角相等时，三层弛豫可以破坏XY平面上的两重旋转对称性。
The incommensurate stacking of multi-layered two-dimensional materials is a challenging problem from a theoretical perspective and an intriguing avenue for manipulating their physical properties. Here we present a multi-scale model to obtain the mechanical relaxation pattern of twisted trilayer van der Waals (vdW) heterostructures with two independent twist angles, a generally incommensurate system without a supercell description. We adopt the configuration space as a natural description of such incommensurate layered materials, based on the local environment of atomic positions, bypassing the need for commensurate approximations. To obtain the relaxation pattern, we perform energy minimization with respect to the relaxation displacement vectors. We use a continuum model in combination with the Generalized Stacking Fault energy to describe the interlayer coupling, obtained from first-principles calculations based on Density Functional Theory. We show that the relaxation patterns of twisted trilayer graphene and $\mathrm{WSe_2}$ are "moire of moire", as a result of the incommensurate coupling two bilayer moire patterns. We also show that, in contrast to the symmetry-preserving in-plane relaxation in twisted bilayers, trilayer relaxation can break the two-fold rotational symmetry about the xy-plane when the two twist angles are equal.