Effective vacua for Floquet topological phases: A numerical perspective on switch-function formalism

Abstract

We propose a general edge index definition for two-dimensional Floquet topological phases based on a switch-function formalism. When the Floquet operator has a spectral gap the index covers both clean and disordered phases, anomalous or not, and does not require the bulk to be fully localized. It is interpreted as a non-adiabatic charge pumping that is quantized when the sample is placed next to an effective vacuum. This vacuum is gap-dependent and obtained from a Floquet Hamiltonian. The choice of a vacuum provides a simple and alternative gap-selection mechanism. Inspired by the model from Rudner et al. we then illustrate these concepts on Floquet disordered phases. Switch-function formalism is usually restricted to infinite samples in the thermodynamic limit. Here we circumvent this issue and propose a numerical implementation of the edge index that could be adapted to any bulk or edge index expressed in terms of switch functions, already existing for many topological phases.

13 pages, 10 figures, Correcting some typos and including an application to a non-anomalous model. To appear in Physical Review B

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Cited by in corpus (11)

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• Strongly Disordered Floquet Topological Systems
• Estimating bulk and edge topological indices in finite open chiral chains
• Local Chern Marker for Periodic Systems
• Chiral Flow in One-dimensional Floquet Topological Insulators
• Topological chiral modes in random scattering networks
• Three dimensional two-band Floquet topological insulator with $Z_2$ index
• Eigenvalue crossings in Floquet topological systems
• Fluctuations and Correlations of Local Topological Order Parameters in Disordered Two-dimensional Topological Insulators
• Real-space formulation of the Chern invariant and topological phases in a disordered Chern insulator