arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2006.09515cond-mat.str-elcond-mat.quant-gas
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晶格对称性与反铁磁量子霍尔态的出现

Lattice symmetry and emergence of antiferromagnetic quantum Hall states

Morad Ebrahimkhas, Mohsen Hafez-Torbati, Walter Hofstetter

摘要:

具有非平凡拓扑带的系统中的强局域相互作用可以稳定量子态,如磁性拓扑绝缘体。我们研究了晶格对称性对可能出现的反铁磁量子霍尔态的影响。我们考虑的Spinful的Harper-Hofstadter模型扩展的下一个最近邻(NNN)跳跃,打开一个间隙在半填充,并允许实现量子霍尔绝缘体。量子霍尔绝缘体具有陈数$\mathcal{C}=2$,因为两个自旋分量处于相同的量子霍尔状态。我们在系统中沿$\hat{x}$方向增加了一个有利于正常绝缘体的交错势$Δ$,并在系统中增加了有利于莫特绝缘体的Hubbard相互作用$U$.莫特绝缘体是一个Néel反铁磁小和条纹反铁磁大NNN跳跃。我们调查的$U$ - $Δ$相图的小和大NNN跳跃模型。结果表明,在大NNN跳变时,相图中存在$\mathcal{C}=1$条状反铁磁量子霍尔绝缘体,而在小NNN跳变时,不存在等效的$\mathcal{C}=1$ Néel反铁磁量子霍尔绝缘体.我们讨论了只有当自旋翻转效应不能被空间群操作补偿时,才能出现$\mathcal{C}=1$反铁磁量子霍尔绝缘体。我们的研究结果可以作为一个指导方针,在未来的研究中寻找反铁磁量子霍尔态。

英文摘要:

Strong local interaction in systems with non-trivial topological bands can stabilize quantum states such as magnetic topological insulators. We investigate the influence of the lattice symmetry on the possible emergence of antiferromagnetic quantum Hall states. We consider the spinful Harper-Hofstadter model extended by a next-nearest-neighbor (NNN) hopping which opens a gap at half-filling and allows for the realization of a quantum Hall insulator. The quantum Hall insulator has the Chern number $\mathcal{C}=2$ as both spin components are in the same quantum Hall state. We add to the system a staggered potential $Δ$ along the $\hat{x}$-direction favoring a normal insulator and the Hubbard interaction $U$ favoring a Mott insulator. The Mott insulator is a Néel antiferromagnet for small and a stripe antiferromagnet for large NNN hopping. We investigate the $U$-$Δ$ phase diagram of the model for both small and large NNN hoppings. We show that while for large NNN hopping there exists a $\mathcal{C}=1$ stripe antiferromagnetic quantum Hall insulator in the phase diagram, there is no equivalent $\mathcal{C}=1$ Néel antiferromagnetic quantum Hall insulator at the small NNN hopping. We discuss that a $\mathcal{C}=1$ antiferromagnetic quantum Hall insulator can emerge only if the effect of the spin-flip transformation cannot be compensated by a space group operation. Our findings can be used as a guideline in future investigations searching for antiferromagnetic quantum Hall states.

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