The light absorption due to the transitions between the edge and two-dimensional (2D) states of a 2D topological insulator (TI) is considered in the Volkov-Pankratov model. It is shown that the transitions are allowed only for the in-plane electric field orthogonal to the edge of the TI. It is found that the absorption is accompanied by the pure spin photocurrent along the TI edge. The possibility of the spin current measurement using polarized luminescence from 2D TI quantum dots is discussed.

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

Quantum corrections to the conductivity of a mesoscopic ring in a nonstationary magnetic field with the flux (t) = V t are investigated. The time dependence of the quantum corrections shows periodic cusps with a period corresponding to the magnetic flux quantum 0 = hc/2e. If the characteristic time of the magnetic flux variation τ 0 = 0 /V is much smaller than the phase relaxation time τ ϕ , the cusps become asymmetrical.

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.