Exploring the nontrivial band edge in the bulk of the topological insulators Bi_{2}Se_{3} and Bi_{2}Te_{3}

Bi_{2}Se_{3} and related compounds are prototype three-dimensional topological insulators with a single Dirac cone in the surface band structure. While the topological surface states can be characterized with surface-sensitive methods, the underlying bulk energy band inversion has not been investigated in detail. Here, a study is presented that combines density-functional theory and nuclear magnetic resonance to explore the nontrivial band edge of Bi_{2}Se_{3} and Bi_{2}Te_{3}. It is found that the topological band inversion is not a discrete reversal of the order of the valence and conduction band at the Γ point. Rather, the bands closest to the Fermi level become well mixed and spread evenly below and above the band gap, such that the characters of the valence- and conduction-band edges become indistinguishable. Beside those bands relevant for the band inversion, i.e., Bi and Se p_{z}, also Bi p_{x} and p_{y} states are involved. As a part of this mixture of states, the band inversion shows no edges in k space.