Optical properties of the doped Bi$_{2}$Te$_{3}$ single crystals: electron-phonon coupling and bulk-boundary correspondence

We studied the optical properties of Bi$_{2}$Te$_{3}$ single crystals doped with La (8{\%}), Ce (8{\%}), Fe(8{\%}, 15{\%}) via a combination of terahertz time-domain spectroscopy and spectroscopic ellipsometry. We observed the Drude peak and the in-plane phonon near 60 cm$^{-1}$ in the optical conductivity in the terahertz regime as well as the absorptions corresponding to the bulk interband transitions in the far-infrared and the visible-ultraviolet regions. We confirmed that the terahertz in-plane phonon asymmetry can be employed as spectroscopic evidence in order to investigate the electron-phonon interaction arising from external dopants while the bulk band structure can be determined from ellipsometry.