Floquet-Bloch Theory and Topology in Periodically Driven Lattices

2013/03/20 by Álvaro Gómez-León, Alvaro Gomez-Leon, Gloria Platero · 21 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum many-body systems #Topological Materials and Phenomena #cond-mat.mes-hall #quant-ph

paper · pdf · doi:10.1103/physrevlett.110.200403

published as Physical Review Letters 110, 200403 (2013) · 5 pages, 6 figures and supplementary information

arxiv created 2013/03/20 · openalex publication_date 2013/05/14 · arxiv updated 2013/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We propose a general framework to solve tight binding models in D dimensional lattices driven by ac electric fields. Our method is valid for arbitrary driving regimes and allows us to obtain effective Hamiltonians for different external field configurations. We establish an equivalence with time-independent lattices in D+1 dimensions and analyze their topological properties. Furthermore, we demonstrate that nonadiabaticity drives a transition from topological invariants defined in D+1 to D dimensions. Our results have potential applications in topological states of matter and nonadiabatic topological quantum computation, predicting novel outcomes for future experiments.

Citations

• Photoinduced Transition between Conventional and Topological Insulators in Two-Dimensional Electronic Systems
• Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field
• Classification of topological insulators and superconductors in three spatial dimensions
• Maximally localized Wannier functions: Theory and applications
• Topological Insulators

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• Floquet engineering of edge states in the presence of staggered potential and interactions
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• 2D Solitons in PT-Symmetric Photonic Lattices
• Random-walk topological transition revealed via electron counting
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• Controlling topological superconductivity by magnetization dynamics
• Dynamically Manipulating Topological Physics and Edge Modes in a Single Degenerate Optical Cavity
• Dissipative Floquet topological systems
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• Floquet-Boltzmann equation for periodically driven Fermi systems
• Chiral symmetry and bulk-boundary correspondence in periodically driven one-dimensional systems
• Merging of Dirac points and Floquet topological transitions in ac-driven graphene

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