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The 2D TI edge states are considered within the Volkov-Pankratov (VP)Hamiltonian. A smooth transition between TI and OI is assumed. The edge statesare formed in the total gap of homogeneous 2D material. A pair of these statesare of linear dispersion, others have gapped Dirac spectra. The opticalselection rules are found. The optical transitions between the neighboring edgestates appear in the global 2D gap for the in-plane light electric fielddirected across the edge.  The electrons in linear edge states have no backscattering, that isindicative of the fact of topological protection. However, when linear edgestates get to the energy domain of Dirac edge states, the backscatteringbecomes permitted. The elastic backscattering rate is found. The Drude-likeconductivity is found when the Fermi level gets into the energy domain of thecoexistence of linear and Dirac edge states. The localization edge conductanceof a finite sample at zero temperature is determined.

Electron states on the smooth edge of 2D topological insulator: elastic backscattering and light absorption