Interband absorption edge in topological insulators Bi$_2$(Te$_{1-x}$Se$_x$)$_3$

TL;DR

This study investigates the optical properties and interband absorption edges of topological insulator thin films Bi$_2$Te$_3$, Bi$_2$Se$_3$, and their alloys, revealing direct bandgap energies and their dependence on composition and Brillouin zone location.

Contribution

It provides experimental evidence for the direct bandgap energies and their locations in the Brillouin zone, supporting recent theoretical GW calculations and clarifying the electronic structure of these topological insulators.

Findings

Bi$_2$Se$_3$ has a direct bandgap of 215 meV at 10 K at the $A0$ point.

Bi$_2$Te$_3$ exhibits a similar direct interband absorption onset at about 200 meV.

The alloy Bi$_2$(Te$_{1-x}$Se$_x$)$_3$ shows maximum interband transition energy near $x=0.3$, indicating a crossover point in the Brillouin zone.

Abstract

We have investigated the optical properties of thin films of topological insulators Bi$_{2}$Te$_{3}$, Bi$_{2}$Se$_{3}$ and their alloys Bi$_2$(Te$_{1-x}$Se$_x$)$_3$ on 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 Bi$_2$Se$_3$, after the correction for the Burstein-Moss effect, we find the value of direct bandgap of $215\pm10$ meV at 10 K. Our data supports the picture that Bi$_2$Se$_3$ has a direct band gap located at the $\Gamma$ 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 Bi$_2$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 $\Gamma$ point but near the Z-F line of the Brillouin zone. In the Bi$_2$(Te$_{1-x}$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 Bi$_2$Te$_2$Se), suggesting that the crossover of the direct interband transitions between the two points in the Brillouin zone occurs close to this composition.