Topological quantum criticality of the disordered Chern insulator

Abstract

We consider the two-dimensional topological Chern insulator in the presence of static disorder. Generic quantum states in this system are Anderson localized. However, topology requires the presence of a subset of critical states, with diverging localization length (the Chern insulator analog of the `center of the Landau band states' of the quantum Hall insulator.) We discuss geometric criteria for the identification of these states at weak disorder, and their extension into the regime of strong disorder by analytical methods. In this way, we chart a critical surface embedded in a phase space spanned by energy, topological control parameter, and disorder strength. Our analytical predictions are supplemented by a numerical analysis of the position of the critical states, and their multifractal properties.

13 pages, 6 figures

References in corpus (6)

• Anderson Transitions
• Topological Anderson Insulator
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• Scaling collapse of longitudinal conductance near the integer quantum Hall transition
• Quartic multifractality and finite-size corrections at the spin quantum Hall transition

Cited by in corpus (7)

• Fragility of surface states in non-Wigner Dyson topological insulators
• Random-Flux-Induced Transition Sequence between Weak and Strong Topological Phases with Anisotropic Localization Properties
• Quantum Hall criticality in an amorphous Chern insulator
• Quantum Hall Effect without Chern Bands
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Dephasing-induced Quantum Hall Criticality in the Quantum Anomalous Hall system
• Phase Transition of Topological Index driven by Dephasing