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Linearity of the topological insulator edge state spectrum plays the crucialrole for various transport phenomena. The previous studies found that thislinearity exists near the spectrum crossing point, but did not determine howperfect the linearity is. The purpose of the present study is to answer thisquestion in various edge states models. We examine Volkov and Pankratov (VP)model [1] for the Dirac Hamiltonian and the model of [2,3] (BHZ1) for theBernevig, Hughes and Zhang (BHZ) Hamiltonian [4] with zero boundary conditions.It is found that both models yield ideally linear edge states. In the BHZ1model the linearity is conserved up to the spectrum ending points correspondingto the tangency of the edge spectrum with the boundary of 2D states. Incontrast, the model of[5] (BHZ2) with mixed boundary conditions for BHZHamiltonian and the 2D tight-binding (TB) model from [4] yield weaknon-linearity.

Linearity of the edge states energy spectrum in the 2D topological insulator