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

نویسندگان

چکیده

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

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ژورنال

عنوان ژورنال: Physical review

سال: 2021

ISSN: ['0556-2813', '1538-4497', '1089-490X']

DOI: https://doi.org/10.1103/physrevb.104.115127