Dynamic bulk-boundary correspondence for anomalous Floquet topology

Abstract

Periodically driven systems with internal and spatial symmetries can exhibit a variety of anomalous boundary behaviors at both the zero and $\pi$ quasienergies despite the trivial bulk Floquet bands. These phenomena are called anomalous Floquet topology (AFT) as they are unconnected from their static counterpart, arising from the winding of the time evolution unitary rather than the bulk Floquet bands at the end of the driving period. In this paper, we systematically derive the first and inversion-symmetric second-order AFT bulk-boundary correspondence for Altland-Zirnbauer (AZ) classes BDI, D, DIII, AII. For each AZ class, we start a dimensional hierarchy with a parent dimension having $\mathbb{Z}$ classification, then use it as an interpolating map to classify the lower-dimensional descendants. From the Atiyah-Hirzebruch spectral sequence (AHSS), we identify the subspace that contains topological information and faithfully derive the AFT bulk-boundary correspondence for both the parent and descendants. Our theory provides analytic tools for out-of-equilibrium topological phenomena.

19 pages, 8 figures

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• Systematic generation of the cascade of anomalous dynamical first and higher-order modes in Floquet topological insulators
• Dynamical construction of Quadrupolar and Octupolar topological superconductors
• Engineering anomalous Floquet Majorana modes and their time evolution in helical Shiba chain
• Floquet second-order topological Anderson insulator hosting corner localized modes
• Stable measurement-induced Floquet enriched topological order
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation
• Bulk-boundary correspondence in topological systems with the momentum dependent energy shift