Anisotropic Topological Anderson Transitions in Chiral Symmetry Classes

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.

4.5 pages with supplemental materials

References in corpus (20)

• Anderson Transitions
• Evidence for an electron nematic phase transition in underdoped iron pnictide superconductors
• Topological nodal line semimetals
• Electronic liquid crystal state in the high-temperature superconductor YBCO(6.45)
• Formation of a Nematic Fluid at High Fields in Sr3Ru2O7
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Topological delocalization of two-dimensional massless Dirac fermions
• Topological surface states in nodal superconductors
• Critical exponent for the quantum Hall transition
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• Second-Order Real Nodal-Line Semimetal in Three-Dimensional Graphdiyne
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
• Thermal metal-insulator transition in a helical topological superconductor
• Scaling collapse of longitudinal conductance near the integer quantum Hall transition
• Quantum Multicriticality in Disordered Weyl Semimetal
• Spectral duality and distribution of exponents for transfer matrices of block tridiagonal Hamiltonians
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes
• Critical Behaviors of Anderson Transitions in Three Dimensional Orthogonal Classes with Particle-hole Symmetries
• Multicriticality of Two-dimensional Class D Disordered Topological Superconductors
• Renormalization group analysis of Dirac fermions with random mass

Cited by in corpus (11)

• Field theory of non-Hermitian disordered systems
• Topological effect on the Anderson transition in chiral symmetry classes
• Universal hard-edge statistics of non-Hermitian random matrices
• Cavity quantum electrodynamics of photonic temporal crystals
• Topological Anderson insulators by latent symmetry
• Half-Quantized Hall Metal and Marginal Metal in Disordered Magnetic Topological Insulators
• Disorder-induced instability of a Weyl nodal loop semimetal towards a diffusive topological metal with protected multifractal surface states
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors
• Non-self-averaging topological Anderson insulator
• Universal localization-delocalization transition in chiral-symmetric Floquet drives