We report a homotopic analysis of quantum states in two-dimensional (2D) polymorphs. Two typical models, namely the honeycomb-type and Shastry-Sutherland-type models, are continuously connected through a deformable herringbone lattice model having a nonsymmorphic group symmetry. The evolution of Dirac fermions is characterized within the phase space spanned by the deformation parameters. Our tight-binding models, based on single orbitals for each site with and without spin-orbit coupling (SOC), reveal how the SOC convolutes, the manner being important in facilitating the search and design of 2D topological insulators focused on the homotopic feature of symmetry-protected properties independent of specific materials.

• Received 2 April 2022
• Revised 24 August 2022
• Accepted 18 October 2022

DOI:https://doi.org/10.1103/PhysRevB.106.195106