Ellipsometric studies of the optical properties of Bi$_{2}$Se$_{3}$ and Bi$_{2}$Se$_{3}\langle$Cu$\rangle$ single crystals

In this work, by spectroscopic ellipsometry the imaginary and real parts of the dielectric function of Bi$_{2}$Se$_{3}$ и Bi$_{2}$Se$_{3}\langle$Cu$\rangle$ single crystals were obtained in the photon energy range from 0.7 eV to 6.5 eV, and were determined the energies of allowed direct transitions responsible for some optical properties. By the help of Cody-Lorentz and Lorentz optical oscillators, the dispersion relation is adjusted in conformity with the experimental data. The values of the refractive index $n$ and the extinction coefficient $k$ of Bi$_{2}$Se$_{3}$ single crystals are calculated in the energy range from 0.7 eV to 6.5 eV. It was also determined that the maximum absorption corresponds to the transitions at 1.900 eV and 1.949 eV for Bi$_{2}$Se$_{3}$ и Bi$_{2}$Se$_{3}\langle$Cu$\rangle$, respectively.