Quantum Hall criticality in Floquet topological insulators

Abstract

The anomalous Floquet Anderson insulator (AFAI) is a two dimensional periodically driven system in which static disorder stabilizes two topologically distinct phases in the thermodynamic limit. The presence of a unit-conducting chiral edge mode and the essential role of disorder induced localization are reminiscent of the integer quantum Hall (IQH) effect. At the same time, chirality in the AFAI is introduced via an orchestrated driving protocol, there is no magnetic field, no energy conservation, and no (Landau level) band structure. In this paper we show that in spite of these differences the AFAI topological phase transition is in the IQH universality class. We do so by mapping the system onto an effective theory describing phase coherent transport in the system at large length scales. Unlike with other disordered systems, the form of this theory is almost fully determined by symmetry and topological consistency criteria, and can even be guessed without calculation. (However, we back this expectation by a first principle derivation.) Its equivalence to the Pruisken theory of the IQH demonstrates the above equivalence. At the same time it makes predictions on the emergent quantization of transport coefficients, and the delocalization of bulk states at quantum criticality which we test against numerical simulations.

arXiv comment15 pages, 5 figures

References in corpus (21)

• Photonic Floquet Topological Insulators
• Anderson Transitions
• Periodic table for topological insulators and superconductors
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Photovoltaic Hall effect in graphene
• Topological characterization of periodically-driven quantum systems
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Observation of topologically protected bound states in a one dimensional photonic system
• Periodic Table for Floquet Topological Insulators
• The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
• Floquet symmetry-protected topological phases in cold atomic systems
• Supersymmetry for Systems with Unitary Disorder: Circular Ensembles
• Quantum Hall effect in a one-dimensional dynamical system
• Quantized magnetization density in periodically driven systems
• The integer quantum Hall plateau transition is a current algebra after all
• Floquet chiral magnetic effect
• Localisation, delocalisation, and topological transitions in disordered 2D quantum walks
• Gaussian free fields at the integer quantum Hall plateau transition
• Emergence of integer quantum Hall effect from chaos
• Sigma models for quantum chaotic dynamics
• Topological Signatures in Quantum Transport in Anomalous Floquet-Anderson Insulators

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• Quantum Hall network models as Floquet topological insulators
• Floquet simulators for topological surface states in isolation
• Anomalous levitation and annihilation in Floquet topological insulators
• Topological delocalization in the completely disordered two-dimensional quantum walk
• Proposal for realizing anomalous Floquet insulators via Chern band annihilation
• Quantitative measure of topological protection in Floquet systems through the spectral localizer
• Quantized charge transport in disordered Floquet topological insulators in the absence of Anderson localization