[论文解读] Relative Stability of Bernal and Rhombohedral Stackings in Trilayer Graphene under Distortions

Raúl Guerrero‐Avilés, M. Pelc+3 more|arXiv (Cornell University)|Oct 13, 2021

Graphene research and applications被引用 2

一句话总结

本研究采用包含范德华相互作用的密度泛函理论（DFT）方法，研究晶格畸变对三层石墨烯中菱面体（ABC）与双层堆叠（ABA）相对稳定性的影响。结果表明，压缩应变、剪切形变以及亚晶格对称性破缺位移可使Bernal堆叠比菱面体堆叠更稳定，能量差最高达0.07 meV，揭示了通过应变和基底工程调控堆叠顺序的关键路径。

ABSTRACT

Stackings in graphene have a pivotal role in properties to be discussed in the future, as seen in the recently found superconductivity of twisted bilayer graphene. Beyond bilayer graphene, the stacking order of multilayer graphene can be rhombohedral, which shows flat bands near the Fermi level that are associated with interesting phenomena, such as tunable conducting surface states expected to exhibit spontaneous quantum Hall effect, surface superconductivity, and even topological order. However, the difficulty in exploring rhombohedral graphenes is that in experiments, the alternative, hexagonal stacking is the most commonly found geometry and has been considered the most stable configuration for many years. Here we reexamine this stability issue in line with current ongoing studies in various laboratories. We conducted a detailed investigation of the relative stability of trilayer graphene stackings and showed how delicate this subject is. These few-layer graphenes appear to have two basic stackings with similar energies. The rhombohedral and Bernal stackings are selected using not only compressions but anisotropic in-plane distortions. Furthermore, switching between stable stackings is more clearly induced by deformations such as shear and breaking of the symmetries between graphene sublattices, which can be accessed during selective synthesis approaches. We seek a guide on how to better control -- by preserving and changing -- the stackings in multilayer graphene samples.

研究动机与目标

• 解决长期以来关于在实际形变条件下，三层石墨烯中菱面体堆叠与Bernal堆叠哪种更稳定的疑问。
• 研究晶格畸变（如压缩、剪切和亚晶格位移）如何影响ABC与异面堆叠之间的能量偏好。
• 为通过应变、基底相互作用及分子修饰实现多层石墨烯堆叠顺序的实验调控提供理论指导。

提出的方法

• 使用VASP软件包进行密度泛函理论（DFT）计算，采用700 Ry的动能截断能和288×288×1的k点网格，中心位于Γ点。
• 采用vdW-DF2泛函以精确描述石墨烯层间的长程范德华相互作用。
• 在固定面内晶胞形状和体积的条件下进行结构弛豫，允许面外离子弛豫以确定基态能量极小值。
• 施加受控的晶格形变：单轴压缩、剪切应变以及原子亚晶格位移，以探测堆叠相变。
• 在各种形变条件下比较ABC与异面堆叠构型的能量，以确定相对稳定性。
• 对k点网格、离子和电子弛豫进行收敛性测试，以确保数值精度。

实验结果

研究问题

• RQ1 在何种条件下，菱面体堆叠在三层石墨烯中变得比Bernal堆叠更不稳定？
• RQ2 压缩、剪切以及亚晶格对称性破缺形变如何影响ABC与ABA堆叠之间的相对能量？
• RQ3 层间相互作用，特别是次近邻原子的作用，在形变条件下决定堆叠稳定性中起到何种作用？
• RQ4 方向性应变或原子位移是否能诱导ABC到ABA堆叠的转变，并产生可测量的能量差？
• RQ5 基底诱导的应变和吸附原子是否可能使一种堆叠比另一种更稳定？

主要发现

• 在原始、无畸变的三层石墨烯基态中，菱面体（ABC）堆叠比Bernal（ABA）堆叠略为稳定。
• 在单轴压缩应变ε < 2.5%时，系统发生从ABC到ABA堆叠的相变，表明压缩应变有利于Bernal堆叠。
• 剪切形变和亚晶格对称性破缺位移引起各向异性的能量差异，当A原子向上位移（或B原子向下位移）时，Bernal堆叠更稳定，能量差最高可达0.07 meV。
• 由于亚晶格位移引起的0.07 meV能量差源于次近邻原子的贡献以及ABA构型中能级的分裂。
• 通过应变或吸附原子实现的亚晶格对称性破缺可稳定Bernal堆叠，表明这是在器件制造中调控堆叠顺序的可行途径。
• 研究结果表明，基底诱导的应变和分子修饰可用于工程化堆叠顺序，从而调控多层石墨烯异质结构的电子性质。