We investigate electronic and transport properties of bismuth (111) bilayer in the context of stability of its topological properties against different perturbations. The effects of spin-orbit coupling variations, geometry relaxation and an interaction with a substrate are considered. Transport properties are studied in the presence of Anderson disorder. Band structure calculations are performed within multi-orbital tight-binding model and density functional theory methods. A band inversion process in bismuth (111) infinite bilayer and an evolution of edge states dispersion in ribbons as a function of spin-orbit coupling strength are analyzed. A significant change of orbital composition of the conduction and valence bands during a topological phase transition is observed. A topological phase is shown to be robust when the effect of geometry relaxation is taken into account. An interaction with a substrate has similar effect to an external perpendicular electric field. The robust quantized conductance is observed when the Fermi energy lies within the bulk energy gap, where only two counter-propagating edge states are present. For energies where the Fermi level crosses more in-gap states, a scattering is possible between channels lying close in $k-$space. When the energy of edge states overlaps with bulk states, no topological protection is observed.
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