A theory of three-dimensional (3D) quasi-localized phases in the chiral symmetry classes

Recently, researchers have discovered that a diffusive metal in chiral symmetry classes with 1D weak topology universally undergoes a disorder-driven quantum phase transition to a "quasi-localized" phase, which exhibits an extreme spatial anisotropy in its transport properties [1,2]. In the quasi-localized phase, the exponential localization length along a spatial direction with the weak topology is divergent, while remains finite along other directions. Remarkably, such quasi-localized phases can also be ubiquitously realized in eigenstates of non-Hermitian operators in the most fundamental symmetry classes [3], indicating its abundant application to open wave systems. In this talk, we will employ a duality mapping of the non-linear sigma model with the weak topology in the three-dimensional (3D) chiral systems, to provide a physical picture and underlying mechanism of the 3D "quasi-localized" phase.

[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, arXiv2402.02310, to appear in Phys. Rev. Lett.

[3] X. Luo, Z. Xiao, K. Kawabata, T. Ohtsuki, and R. Shindou, Phys. Rev. Research, 4 L022035 (2022).