  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.
