Liu Xiaoqian, Peng Ran, Sun Zhaoru, Liu Jianpeng
School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China.
ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China.
Nano Lett. 2022 Oct 12;22(19):7791-7797. doi: 10.1021/acs.nanolett.2c02010. Epub 2022 Sep 28.
Magic-angle twisted bilayer graphene (TBG) has attracted significant interest recently due to the discoveries of diverse correlated and topological states. In this work, we study the phonon properties in magic-angle TBG based on many-body classical potential and interatomic forces generated by a deep neural network trained with data from calculations. We have discovered a number of soft modes which can exhibit dipolar, quadrupolar, and octupolar vibrational patterns in real space, as well as some time-reversal breaking chiral phonon modes. We have further studied the phonon effects on the electronic structures by freezing certain soft phonon modes. We find that if a soft quadrupolar phonon mode is assumed to be frozen, the system would exhibit a charge order which is perfectly consistent with recent experiments. Moreover, once some low-frequency -breaking modes get frozen, the Dirac points at the charge neutrality point would be gapped out, which provides an alternative perspective to the origin of correlated insulator state at charge neutrality point.
魔角扭曲双层石墨烯（TBG）由于多种关联和拓扑态的发现，近来引起了广泛关注。在这项工作中，我们基于多体经典势以及由深度神经网络根据计算数据训练生成的原子间力，研究了魔角TBG中的声子性质。我们发现了许多软模，它们在实空间中可呈现偶极、四极和八极振动模式，以及一些时间反演破缺的手性声子模式。我们通过冻结某些软声子模式，进一步研究了声子对电子结构的影响。我们发现，如果假设一个软四极声子模式被冻结，系统将呈现出与近期实验完全一致的电荷序。此外，一旦一些低频破缺模式被冻结，电荷中性点处的狄拉克点将出现能隙，这为电荷中性点处关联绝缘体态的起源提供了一个不同的视角。
