Elastic backscattering of edge electrons and light absorption on a smooth edge of a 2D topological insulator

2D topological insulator edge states are considered within the Volkov-Pankratov Hamiltonian. A smooth transition between a topological and ordinary insulator is assumed. The edge states are formed in the total gap of homogeneous 2D material. We found the energy spectrum, wave functions, together with the matrix elements of the impurity potential, and the velocity operator between these states. A pair of states have linear dispersion (the Weyl states), others have gapped Dirac spectra. Optical selection rules are found. It is stated that the Weyl states do not experience the backscattering, while the elastic scattering is permitted between the Dirac states or between the Weyl and Dirac states.