Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices

Higher-order topological states that possess gapped bulk energy bands and exotic topologically protected boundary states with at least two dimensions lower than the bulk have opened a significant and new perspective for understanding topological quantum matter. Here, we propose to generate two-dimensional (2D) topological boundary states for implementing a synthetic magnetic flux of ultracold atoms trapped in bilayer optical lattices. It is shown that a Chern insulator, Dirac semimetals, and a second-order topological phase (SOTP) are generated by the interplay of the two-photon detuning and effective Zeeman shift. These observed topological phases can be well characterized by the energy gap of the bulk, the Wilson loop spectra, and the spin textures at the high-symmetry points of the system. We show that the SOTP exhibits a pair of 0D boundary states. Meanwhile, the phases of the Dirac semimetals and Chern insulator support the conventional 1D boundary states due to the principle of bulk-boundary correspondence. Strikingly, the boundary states that emerge for Dirac semimetals and the SOTP are topologically protected by PT symmetry and chiral-mirror symmetry (M-alpha), respectively. In particular, the location of 0D corner states for the SOTP which are associated with M-alpha symmetry are highly manipulable by tuning the magnetic flux. Our scheme herein provides a platform for emerging exotic topological boundary states, which may facilitate the study of higher-order topological phases in ultracold atomic gases.

Automated summary

This study proposes a method to implement synthetic magnetic flux through two-dimensional topological boundary states in a bilayer optical lattice. By adjusting the two-photon detuning and effective Zeeman shift, Chern insulator, Dirac semimetals, and second-order topological phase (SOTP) are generated. These topological phases can be well characterized by the energy gap of the bulk, the Wilson loop spectra, and the spin textures. The scheme provides a platform for emerging exotic topological boundary states.