AI 中文总结
本研究探究具有交错磁通的三角Hofstadter模型的拓扑性质与相图，利用二聚化破坏平移对称性得到不同q值下的相图特征，结果可在多种实验体系中验证。
AI 中文摘要
本工作研究相邻三角形中具有交错磁通的三角Hofstadter模型的拓扑性质与相图，该晶格可用于描述一定层间电位移场范围内的转角双层过渡金属二硫化物（TMD）的低能物理。我们表明，该模型的Hofstadter谱通常是不对称的，仅当特定交错磁通满足3φ=π/2 mod π时，因存在额外的P对称性而对称。通过二聚化破坏平移对称性会解除P对称性，使系统呈现丰富的拓扑相。具有不同有理外磁通Φ_B=2πp/q的二聚化模型的相图具有以下共同特征：当q为偶数时，二聚化模型通常存在三个有能隙区域，其中二聚化程度小的区域具有有限陈数，另外两个区域陈数为零；当q为奇数时，在任何有限二聚化下模型均为有能隙且陈数为零。对于q为偶数和奇数的情况，两个陈数为零的区域可通过系统在φ=0 mod π/3处的参数化一维链的反演对称性进一步表征，其中一个区域拓扑非平凡，另一个为拓扑平凡。我们的结果可在弱相互作用的转角双层TMD、近期实验实现的光晶格中的冷原子系统或光子晶体中得到验证。
英文摘要
We study the topological properties and phase diagram of the triangular Hofstadter model with staggered flux in adjacent triangles in this work. This lattice can be used to describe the low energy physics of the twisted bilayer transition metal dichalcogenides (TMD) in a certain range of the electric displacement field between the two layers. We show that the Hofstadter spectrum of this model is generally asymmetric except at specific staggered flux $3ϕ= π/2 \mod π$ due to an additional P symmetry at such $ϕ$. Breaking the translation symmetry by dimerization lifts the P symmetry and results in rich topological phases in the system. The dimerized model with different rational external magnetic flux $Φ_B = 2πp/q$ has phase diagram with the following common features. For even q, the dimerized model generally has three gapped regimes. The one with small dimerization has finite Chern number and the other two have zero Chern number. For odd q, the model is gapped with zero Chern number at any finite dimerization. For both q even and odd, the two regimes with zero Chern number can be further characterized by the inversion symmetry of the parametrized one-dimensional chains of the system at ϕ= 0 \mod π/3$, and one regime is topologically non-trivial and the other is trivial. Our results may be tested in twisted bilayer TMD with weak interaction or cold atom systems in optical lattice or photonic crystals achieved in recent experiments.
