Effect of two-dimensional weak topology on Anderson Transitions in Non-Standard Symmetry Classes

While recent studies [1,2] have shown that one-dimensional weak topology induces a novel quasi-localized phase with spatially anisotropic transport properties in both two- and three-dimensional (2D and 3D) chiral symmetry classes, the effect of 2D weak topology on the delocalized-localized transition remains unexplored. In this work, we study a 3D layered Chern insulator lattice model in the Bogoliubov-de-Gennes class C with 2D weak topology, and investigate the behavior of the localization length in both topological plane and non-topological direction under increasing disorder. Numerical results show that along the non-topological direction, the system undergoes two phase transitions: from a Weyl semimetal to a diffusive metal (DM), and from the DM to an Anderson insulator. We evaluate the critical exponent at the latter transition and compare it with that of the class-C model without the 2D weak topology [3]. We further analyze the scaling behavior of the localization length in the topological plane to explore the possible anisotropic effects arising from the 2D weak topology.

[1] Z. Xiao, K. Kawabata, X. Luo, T. Ohtsuki, and R. Shindou, Phys. Rev. Lett. 131, 056301 (2023).

[2] P. Zhao, Z. Xiao, Y. Zhang, and R. Shindou, Phys. Rev. Lett. 133, 226601 (2024).

[3] T. Wang, T. Ohtsuki, and R. Shindou, Phys. Rev. B 104, 014206 (2021).