Journal
PHYSICAL REVIEW B
Volume 104, Issue 11, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.104.115127
Keywords
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Funding
- Air Force Office of Scientific Research [FA9550-20-1-0115]
- U.S. Office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) [N00014-20-1-2325]
- U.S. Army Research Office through the Institute for Soldier Nanotechnologies at MIT [W911NF-18-2-0048]
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In this theoretical study, a three-dimensional Hofstadter model with linearly varying non-Abelian gauge potentials along all dimensions is introduced and analyzed. The model can be interpreted as spin-orbit coupling among a trio of Hofstadter butterfly pairs. It is found that under different choices of gauge fields, both weak and strong topological insulating phases can be identified in the model.
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.
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