Pseudomagnetic fields, particle-hole asymmetry, and microscopic effective continuum Hamiltonians of twisted bilayer graphene
Pseudomagnetic fields, particle-hole asymmetry, and microscopic effective continuum Hamiltonians of twisted bilayer graphene
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DOI：
10.1103/physrevb.107.075408
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发表时间：
2022-08
影响因子：
3.7
通讯作者：
Jian Kang;O. Vafek
中科院分区：
文献类型：
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作者：
Jian Kang;O. Vafek
利用该方法，我们构建了两种不同的扭曲双层石墨烯微观紧束缚模型的有效连续理论，一种是基于Slater Koster的，另一种是基于从头算Wannier的，扭曲角为1.05 ^\circ $.从连续介质理论得到的能谱-无论是刚性扭曲或包括晶格松弛-被发现是在几乎完美的协议，从紧束缚模型的光谱时，梯度展开进行到二阶，证明了该方法的有效性。我们还分析了由此产生的窄带的布洛赫状态的属性，发现不可忽略的粒子-空穴对称性破缺附近的$\Gamma$点在我们的连续理论构造的从头算微观模型由于一个长期的连续理论，以前被忽视。这揭示了与所有现有的连续介质模型的区别，其中窄带希尔伯特空间的粒子-空穴对称性几乎是完美的。
Using the method developed in the companion paper, we construct the effective continuum theories for two different microscopic tight binding models of the twisted bilayer graphene at the twist angle of $1.05^\circ$, one Slater-Koster based and the other ab-initio Wannier based. The energy spectra obtained from the continuum theory -- either for rigid twist or including lattice relaxation -- are found to be in nearly perfect agreement with the spectra from the tight binding models when the gradient expansion is carried out to second order, demonstrating the validity of the method. We also analyze the properties of the Bloch states of the resulting narrow bands, finding non-negligible particle-hole symmetry breaking near the $\Gamma$ point in our continuum theory constructed for the ab-initio based microscopic model due to a term in the continuum theory that was previously overlooked. This reveals the difference with all existing continuum models where the particle-hole symmetry of the narrow band Hilbert space is nearly perfect.