  Linearity of the topological insulator edge state spectrum plays the crucial
role for various transport phenomena. The previous studies found that this
linearity exists near the spectrum crossing point, but did not determine how
perfect the linearity is. The purpose of the present study is to answer this
question 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 the
Bernevig, Hughes and Zhang (BHZ) Hamiltonian [4] with zero boundary conditions.
It is found that both models yield ideally linear edge states. In the BHZ1
model the linearity is conserved up to the spectrum ending points corresponding
to the tangency of the edge spectrum with the boundary of 2D states. In
contrast, the model of[5] (BHZ2) with mixed boundary conditions for BHZ
Hamiltonian and the 2D tight-binding (TB) model from [4] yield weak
non-linearity.
