The Hofstadter model exemplifies a large class of physical systems characterized by particles hopping on a lattice immersed in a gauge field. Recent advancements on various synthetic platforms have enabled highly controllable simulations of such systems with tailored gauge fields featuring complex spatial textures. These synthetic gauge fields could introduce synthetic symmetries that do not appear in electronic materials. Here, in an $\mathrm{SU}\left(2\right)$ non-Abelian Hofstadter model, we theoretically show the emergence of multiple nonsymmorphic chiral symmetries, which combine an internal unitary antisymmetry with fractional spatial translation. Depending on the values of the gauge fields, the nonsymmorphic chiral symmetries can exhibit non-Abelian algebra and protect Kramers quartet states in the bulk band structure, creating general fourfold degeneracy at all momenta. These nonsymmorphic chiral symmetries protect double Dirac semimetals at zero energy, which become gapped into quantum confined insulating phases upon introducing a boundary. Moreover, the parity of the system size can determine whether the resulting insulating phase is trivial or topological. Our work indicates a pathway for creating topology via synthetic symmetries emergent from synthetic gauge fields.

Close

PrevNext

View figure in article

• Synthetic gauge fields
• Topological effects in photonic systems
• Topological insulators
• Chiral symmetry