Transport phenomena lie at the heart of physics, and emergent anisotropic transports have long played an important role in the development of condensed matter physics [1]. In a recent paper published in Physical Review Letters [2], Xiao et. al. uncovered for the first time that an interplay between band topology and disorder induces a new thermodynamic quasi-localized phase, where a wave function is delocalized along one spatial direction but exponentially localized in the other two spatial directions in contrast with the conventional diffusive metal and localized phases. The emergence of the quasi-localized phase breaks a common belief in physics that the exponential localization of a wave function occurs simultaneously in all the spatial directions. In the quasi-localized phase, conductance along the divergent length scale takes finite values with a non-Ohmic scaling, while the conductance along the other directions are vanishing in the thermodynamic limit. In the manuscript, Xiao et. al. established these findings by precise evaluations of correlation-length critical exponents, critical disorder strengths, and two-terminal conductance of several different models with and without the band topology. To generalize the concept of the quasi-localized phase, they have further introduced a lower-dimensional inverse participation ratio and derive a criterion for the existence/absence of the quasi-localized phase in arbitrary spatial dimensions and symmetry classes.

      In addition to the discovery of the quasi-localized phase, the paper has also uncovered for the first time a novel universality class of the Anderson transition induced by the topology. Classification of phase transitions is one of the ultimate goals of physics, and the Anderson transition is one of the most important phase transitions in both theory and experiment. In fact, the transport phenomena in disordered topological systems have been intensively explored during the past few decades in solid-state, atomic, molecular and optical systems. Nonetheless, the role of the band topology in the Anderson transition has still been elusive [3]. In the manuscript, Xiao et.al. have clarified for the first time a new universality class of the Anderson transition induced by the topology. Topology-induced distinct critical exponents in the same symmetry class and in the same spatial dimension has never been reported, despite the long research history of the Anderson transitions.

      The paper is published online in Physical Review Letters on the second of August [2]. Zhenyu Xiao (graduate student in ICQM, school of Physics, Peking University) is the first author, and Dr. Ryuichi Shindou (faculty member in ICQM, school of Physics, Peking University) is the corresponding author. The work was done in collaboration with Dr. Kohei Kawabata (a former postdoc in Princeton University), Dr. Xunlong Luo (a former ICQM graduate student) and Prof. Tomi Ohtsuki (a faculty member in Sophia University). The work by Zhenyu Xiao, and Ryuichi Shindou was supported by National Basic Research Programs of China (No. 2019YFA0308401) and by National Natural Science Foundation of China (No. 11674011 and No. 12074008).

      [1] E. Fradkin, S. A. Kivelson, M. J. Lawler, J. P. Eisenstein, and A. P. Mackenzie, Nematic Fermi Fluids in Condensed Matter Physics, Annu. Rev. Condens. Matter Phys. 1, 153 (2010).

      [2] Zhenyu Xiao, Kohei Kawabata, Xunlong Luo, Tomi Ohtsuki, and Ryuichi Shindou, Anisotropic topological Anderson transition in chiral symmetry classes, Phys. Rev. Lett. 131, 056301 (2023).

      [3] F. Evers, and A. D. Mirlin, Anderson transitions, Rev. Mod. Phys. 80, 1355 (2008).