Twisted bilayer graphene. II. Stable symmetry anomaly
Twisted bilayer graphene. II. Stable symmetry anomaly
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DOI：
10.1103/physrevb.103.205412
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发表时间：
2020-09
影响因子：
3.7
通讯作者：
Zhida Song;Biao Lian;N. Regnault;B. Bernevig
中科院分区：
文献类型：
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作者：
Zhida Song;Biao Lian;N. Regnault;B. Bernevig
我们证明了具有粒子-空穴对称性的扭曲双层石墨烯(TBG)(而不仅仅是两个活性带)的整个连续模型是反常的，因此与晶格模型不相容。以前的作品，例如[Song et al.，Phys.莱特牧师。123,036401(2019年)]，[Ahn等人，Phys.[Rev.X9,021013(2019年)]，[Po等人，Phys.Rev.B99,195455(2019年)]，以及其他[Kang等人]。太棒了。Rev.X 8,031088(2018年)，Koshino等人，Phys.版本8,031087(2018年)，刘等人，Phys.B修订版，155415(2019年)，邹某等人，Phys.Rev.B98,085435(2018年)]发现TbG中的两个flAt带具有受C2zT对称性保护的脆弱拓扑。[Song et al，Phys.莱特牧师。123,036401(2019年)]还指出了边界层气体连续模型的近似粒子-空穴对称性(P)。在这项工作中，我们数值地相信P确实是fi的一个很好的近似，并证明了两个fl在带的脆弱拓扑被增强到P-保护的稳定拓扑。这个稳定的拓扑意味着中间两个带之间有4个L+2(L∈N)狄拉克点。P保护的稳定拓扑对中间两个频带和其他频带之间的任意间隙闭合是健壮的。我们进一步证明，值得注意的是，这种P保护的稳定拓扑以及相应的4个L+2狄拉克点不能在同时保持C2zT和P对称性的格子模型中实现。换言之，TBG的连续模型是反常的，不能在晶格上实现。文中还讨论了另外两个与拓扑有关的问题，即两个flAt带中陈能带基团的选择和所谓第二手性极限中理想金属相的选择。
We show that the entire continuous model of twisted bilayer graphene (TBG) (and not just the two active bands) with particle-hole symmetry is anomalous and hence incompatible with lattice models. Previous works, e.g. , [Song et al., Phys. Rev. Lett. 123, 036401 (2019)], [Ahn et al., Phys. Rev. X 9, 021013 (2019)], [Po et al., Phys. Rev. B 99, 195455 (2019)], and others [Kang et al. Phys. Rev. X 8, 031088 (2018), Koshino et al., Phys. Rev. X 8, 031087 (2018), Liu et al., Phys. Rev. B 99, 155415 (2019), Zou et al., Phys. Rev. B 98, 085435 (2018)] found that the two flat bands in TBG possess a fragile topology protected by the C 2 z T symmetry. [Song et al., Phys. Rev. Lett. 123, 036401 (2019)] also pointed out an approximate particle-hole symmetry ( P ) in the continuous model of TBG. In this work, we numerically confirm that P is indeed a good approximation for TBG and show that the fragile topology of the two flat bands is enhanced to a P -protected stable topology. This stable topology implies 4 l + 2 ( l ∈ N ) Dirac points between the middle two bands. The P -protected stable topology is robust against arbitrary gap closings between the middle two bands the other bands. We further show that, remarkably, this P -protected stable topology, as well as the corresponding 4 l + 2 Dirac points, cannot be realized in lattice models that preserve both C 2 z T and P symmetries. In other words, the continuous model of TBG is anomalous and cannot be realized on lattices. Two other topology related topics, with consequences for the interacting TBG problem, i.e. , the choice of Chern band basis in the two flat bands and the perfect metal phase of TBG in the so-called second chiral limit, are also discussed.