Quantized magnetization density in periodically driven systems

Abstract

We study micromotion in two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We show that this micromotion gives rise to a quantized time-averaged magnetization density when the system is filled with fermions. Furthermore we find that a quantized current flows around the boundary of any filled region of finite extent. The quantization has a topological origin: we relate the time-averaged magnetization density to the winding number characterizing the new phase identified in Phys. Rev. X 6, 021013 (2016). We thus establish that the winding number invariant can be accessed directly in bulk measurements, and propose an experimental protocol to do so using interferometry in cold atom based realizations.

5 pages, 3 figures. Supplement: 7 pages, 1 figure

References in corpus (15)

• Photovoltaic Hall effect in graphene
• Topological characterization of periodically-driven quantum systems
• Observation of a Discrete Time Crystal
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems
• Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Disorder-induced Floquet Topological Insulators
• Effective Theory of Floquet Topological Transitions
• Modulated Floquet Topological Insulators
• Topological index for periodically driven time-reversal invariant 2D systems
• Chiral Floquet Phases of Many-body Localized Bosons
• Floquet Topological Order in Interacting Systems of Bosons and Fermions
• Materials design from non-equilibrium steady states: driven graphene as a tunable semiconductor with topological properties
• Optical Control of Topological Quantum Transport in Semiconductors

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