Effective continuum model for relaxed twisted bilayer graphene and moire electron-phonon interaction
Effective continuum model for relaxed twisted bilayer graphene and moire electron-phonon interaction
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松弛扭曲双层石墨烯和莫尔电子声子相互作用的有效连续介质模型
DOI：
10.1103/physrevb.101.195425
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发表时间：
2020
影响因子：
3.7
通讯作者：
Nam Nguyen N. T.
中科院分区：
文献类型：
--
作者：
Koshino Mikito;Nam Nguyen N. T.
我们构建了一个解析连续介质模型来描述具有任意晶格变形的扭曲双层石墨烯中的电子结构和电子-声子相互作用。从紧束缚模型出发，我们推导了一般晶格位移存在下的层间哈密顿量，并获得了平滑变形的长波长连续体表达式。我们证明连续介质模型正确地描述了晶格松弛扭曲双层石墨烯的能带结构。我们将该公式应用于声子振动，并推导了莫尔带态和莫尔声子模式之间的电子声子矩阵元素的显式表达式。通过数值计算，我们发现由于超晶格杂化，电子声子耦合在低扭转角下显着增强。特别是在魔角处，声子介导的电子-电子相互作用被发现与反态密度的量级相当，表明该系统处于强耦合状态。
We construct an analytic continuum model to describe the electronic structure and the electron-phonon interaction in twisted bilayer graphenes with arbitrary lattice deformation. Starting from the tight-binding model, we derive the interlayer Hamiltonian in the presence of general lattice displacement and obtain a long-wavelength continuum expression for smooth deformation. We show that the continuum model correctly describes the band structures of the lattice-relaxed twisted bilayer graphenes. We apply the formula to the phonon vibration and derive an explicit expression of the electron-phonon matrix elements between the moiré band states and the moiré phonon modes. By numerical calculation, we find that the electron-phonon coupling is significantly enhanced in low twist angles due to the superlattice hybridization. At the magic angle, in particular, the phonon-mediated electron-electron interaction is found to be comparable to the order of the inverse density of states, suggesting that the system is in the strong coupling regime.