Edge states on the curved boundary of a 2D topological insulator

The adiabatic 2 × 2 Hamiltonian for the edge states on the curved boundary of a 2D topological insulator (TI) is deduced from the 4 × 4 Volkov-Pankratov Hamiltonian of 2D TI. The self-energy obeys linear dependence on the edge momentum. It is shown that in the case of a close edge the longitudinal momentum is quantized by 2π(n+ 1/2)h/L, where L is the edge length, n is integer. The results are supported by the exact solution of the Schrödinger equation for the TI disk inserted into an ordinary 2D insulator.