论文标题
用于构建通用双层石墨烯中电子有效模型的理论
Theory for constructing effective models for electrons in generic bilayer graphene
论文作者
论文摘要
我们详细介绍和讨论实践技术，以制定有效模型来描述通用双层石墨烯中低能电子的动力学。从使用$ p_z $轨道作为表示基础的$ P_Z $轨道的紧密结合模型开始，我们将其重新将其重新制定为在每个石墨烯层中定义的Bloch状态之间耦合的问题。这种方法允许将原始问题转移到两个独立材料层和此类状态的耦合规则中的BLOCH状态的确定中。我们显示了两个方案来参数化耦合的Bloch状态向量。对于适用长波长近似的小扭曲角的双层石墨烯构型，我们表明有效的汉密尔顿人可以以动量操作员定义的动力学项的规范形式写入，并由位置操作员定义的潜在术语。在数值上讨论了不同复杂水平的有效模型及其在治疗各种物理方面的潜在应用的有效性。
We present and discuss in detail practical techniques in formulating effective models to describe the dynamics of low-energy electrons in generic bilayer graphene. Starting from a tight-binding model using the $p_z$ orbital of carbon atoms as a representation basis set, we reformulate it into the problem of coupling between Bloch states defined in each graphene layer. This approach allows transferring the original problem into the determination of Bloch states in two independent material layers and coupling rules of such states. We show two schemes to parameterize coupled Bloch state vectors. For the bilayer graphene configurations of small twist angle in which the long wavelength approximation is applicable, we show that an effective Hamiltonian can be written in the canonical form of a kinetic term defined by the momentum operator and a potential term defined by the position operator. The validity of effective models of different sophistication levels and their potential application in treating various physical aspects are numerically discussed.
