Three-dimensional non-Abelian generalizations of the Hofstadter model: Spin-orbit-coupled butterfly trios

Article

关键词: TOPOLOGICAL EDGE STATES;    DIRAC FERMIONS;   

DOI  :  10.1103/PhysRevB.104.115127

来源: SCIE

【 摘 要 】

We theoretically introduce and study a three-dimensional Hofstadter model with linearly varying non-Abelian gauge potentials along all three dimensions. The model can be interpreted as spin-orbit coupling among a trio of Hofstadter butterfly pairs since each Cartesian surface (xy, yz, or zx) of the model reduces to a two-dimensional non-Abelian Hofstadter problem. By evaluating the commutativity among arbitrary loop operators around all axes, we derive its genuine (necessary and sufficient) non-Abelian condition, namely, that at least two out of the three hopping phases should be neither 0 nor pi. Under different choices of gauge fields in either the Abelian or the non-Abelian regime, both weak and strong topological insulating phases are identified in the model.

【 授权许可】

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