Topological properties of C_4zT-symmetric semimetals

Two-dimensional topological semimetals are typically characterized by the vorticity of gapless points, and can be classified according to the band representations. However, the topological properties involving the distribution of the Berry curvature in the entire Brillouin zone are often overlooked. In this study, we investigate a two-band two-dimensional topological semimetal protected by C_4zT magnetic symmetry, exhibiting a two-fold band degeneracy at the Γ(0, 0) and M(π, π) points. Due to the presence of C_4zT symmetry, the Brillouin zone is divided into two patches characterized by half-quantized Berry curvature fluxes with opposite signs. In multi-band case, the half-quantization deviates, indicating the fragile nature. The semimetal presents counter-propagating half-edge channels, accompanied by power-law decaying and oscillating edge currents. The band topology leads to unconventional Landau levels featuring anisotropic edge modes. Each massless Dirac cone, associated with the half-quantized Berry curvature flux, exhibits an integer quantum Hall conductance. Additionally, we calculate the local orbital magnetization with open boundary conditions in both the x and y directions. This reveals isolated magnetization islands, highlighting an experimentally observable magnetic phenomenon in this topological semimetal.