The theoretical analysis of topological insulators (TIs) has been traditionally focused on infinite homogeneous crystals with band gap in the bulk and nontrivial topology of their wavefunctions, or infinite wires whose boundaries host surface or edge metallic states. However, experimental devices contain finite-size topological region attached to normal metal (NM) leads, which poses a question about how precise is quantization of longitudinal conductance and how electrons transition from topologically trivial NM leads into the edge states. This is particularly pressing issues for recently conjectured two-dimensional (2D) Floquet TI where electrons flow from time-independent NM leads into time-dependent edge states---the very recent experimental realization of Floquet TI using graphene irradiated by circularly polarized light did not exhibit either quantized longitudinal or Hall conductance. Here we employ charge conserving solution for Floquet-nonequlibrium Green functions (NEGFs) of irradiated graphene nanoribbon to compute longitudinal two-terminal conductance, as well as spatial profiles of local current density as electrons propagate from NM leads into the Floquet TI. In the case of Floquet TI both bulk and edge local current densities contribute equally to total current, which leads to longitudinal conductance below the expected quantized plateau that is slightly reduced by edge vacancies. We propose two experimental schemes to detect coexistence of bulk and edge current densities within Floquet TI: (i) drilling a nanopore in the interior of irradiated region of graphene will induce backscattering of bulk current density, thereby reducing longitudinal conductance by $sim 28$%; (ii) imaging of magnetic field produced by local current density using diamond NV centers.
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