Anisotropic Topological Anderson Transitions in Chiral Symmetry Classes

TL;DR

This paper investigates topological Anderson transitions in 3D disordered systems with chiral symmetry, revealing a new quasi-localized phase with anisotropic transport properties and distinct critical exponents influenced by weak topological indices.

Contribution

It uncovers a universal quasi-localized phase in chiral classes with weak topological indices and characterizes its unique critical behavior and anisotropic transport phenomena.

Findings

Identification of a quasi-localized phase with anisotropic wave function localization.

Different critical exponents for transitions involving the quasi-localized phase.

Manifestation of the phase in anisotropic transport in topological insulators and semimetals.

Abstract

We study quantum phase transitions of three-dimensional disordered systems in the chiral classes (AIII and BDI) with and without weak topological indices. We show that the systems with a nontrivial weak topological index universally exhibit an emergent thermodynamic phase where wave functions are delocalized along one spatial direction but exponentially localized in the other two spatial directions, which we call the quasi-localized phase. Our extensive numerical study clarifies that the critical exponent of the Anderson transition between the metallic and quasi-localized phases, as well as that between the quasi-localized and localized phases, are different from that with no weak topological index, signaling the new universality classes induced by topology. The quasi-localized phase and concomitant topological Anderson transition manifest themselves in the anisotropic transport phenomena of disordered weak topological insulators and nodal-line semimetals, which exhibit the metallic behavior in one direction but the insulating behavior in the other directions.