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arXiv · 2010.11308

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

Vincent Liu·Yi Yang·John D. Joannopoulos·Marin Soljačić
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Abstract

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, 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.

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Vincent Liu, Yi Yang, John D. Joannopoulos, Marin Soljačić. 2020-10-21. Three-dimensional non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly trios. https://doi.org/10.1103/physrevb.104.115127

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