Interband absorption edge in the topological insulators Bi2(Te1−xSex)3

We have investigated the optical properties of thin films of topological insulators ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, and their alloys ${\mathrm{Bi}}_{2}{({\mathrm{Te}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x})}_{3}$ on ${\mathrm{BaF}}_{2}$ substrates by a combination of infrared ellipsometry and reflectivity in the energy range from 0.06 to 6.5 eV. For the onset of interband absorption in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, after the correction for the Burstein-Moss effect, we find the value of the direct band gap of $215\ifmmode\pm\else\textpm\fi{}10$ meV at 10 K. Our data support the picture that ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ has a direct band gap located at the $\mathrm{\ensuremath{\Gamma}}$ point in the Brillouin zone and that the valence band reaches up to the Dirac point and has the shape of a downward-oriented paraboloid, i.e., without a camel-back structure. In ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, the onset of strong direct interband absorption at 10 K is at a similar energy of about 200 meV, with a weaker additional feature at about 170 meV. Our data support the recent $GW$ band-structure calculations suggesting that the direct interband transition does not occur at the $\mathrm{\ensuremath{\Gamma}}$ point but near the $Z\text{\ensuremath{-}}F$ line of the Brillouin zone. In the ${\mathrm{Bi}}_{2}{({\mathrm{Te}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x})}_{3}$ alloy, the energy of the onset of direct interband transitions exhibits a maximum near $x=0.3$ (i.e., the composition of ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}\mathrm{Se}$), suggesting that the crossover of the direct interband transitions between the two points in the Brillouin zone occurs close to this composition.