Bulk-Edge correspondence for two-dimensional Floquet topological insulators

Abstract

Floquet topological insulators describe independent electrons on a lattice driven out of equilibrium by a time-periodic Hamiltonian, beyond the usual adiabatic approximation. In dimension two such systems are characterized by integer-valued topological indices associated to the unitary propagator, alternatively in the bulk or at the edge of a sample. In this paper we give new definitions of the two indices, relying neither on translation invariance nor on averaging, and show that they are equal. In particular weak disorder and defects are intrinsically taken into account. Finally indices can be defined when two driven sample are placed next to one another either in space or in time, and then shown to be equal. The edge index is interpreted as a quantized pumping occurring at the interface with an effective vacuum.

28 pages, 5 figures Minor changes, update and addition of some references To appear in Annales Henri Poincaré

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• Universal quantum criticality in static and Floquet-Majorana chains
• Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system
• Microlocal analysis of the bulk-edge correspondence
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• Strongly Disordered Floquet Topological Systems
• Time-dependent topological systems: A study of the Bott index
• Estimating bulk and edge topological indices in finite open chiral chains
• Characterization of edge states in perturbed honeycomb structures
• Topological chiral modes in random scattering networks
• Effective vacua for Floquet topological phases: A numerical perspective on switch-function formalism
• Chiral Flow in One-dimensional Floquet Topological Insulators
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• Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena
• Universal edge transport in interacting Hall systems
• Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory
• Chiral Floquet systems and quantum walks at half period
• Out of equilibrium chiral higher order topological insulator on a $\pi$-flux square lattice
• Wave-packet propagation in a finite topological insulator and the spectral localizer index
• Unsupervised identification of Floquet topological phase boundaries
• Three dimensional two-band Floquet topological insulator with $Z_2$ index
• Nonlinear signatures of Floquet band topology
• Floquet topological phase transitions induced by uncorrelated or correlated disorder
• Eigenvalue crossings in Floquet topological systems
• Steering edge currents through a Floquet topological insulator
• Classification of unitary operators by local generatability
• Analytic bulk-edge connection in circular-symmetric models
• Chirality induced Interface Currents in the Chalker Coddington Model
• Engineering stable quantum currents at bulk boundaries
• Universal localization-delocalization transition in chiral-symmetric Floquet drives
• The Bott index of two unitary operators and the integer quantum Hall effect
• Examples for stable quantum currents