Exploring the nontrivial band edge in the bulk of the topological insulators Bi2Se3 and Bi2Te3

<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>Bi</a:mi><a:mn>2</a:mn></a:msub><a:msub><a:mi>Se</a:mi><a:mn>3</a:mn></a:msub></a:mrow></a:math> 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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>Bi</b:mi><b:mn>2</b:mn></b:msub><b:msub><b:mi>Se</b:mi><b:mn>3</b:mn></b:msub></b:mrow></b:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>Bi</c:mi><c:mn>2</c:mn></c:msub><c:msub><c:mi>Te</c:mi><c:mn>3</c:mn></c:msub></c:mrow></c:math>. It is found that the topological band inversion is not a discrete reversal of the order of the valence and conduction band at the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi mathvariant="normal">Γ</d:mi></d:math> 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>p</f:mi><f:mi mathvariant="normal">z</f:mi></f:msub></f:math>, also Bi <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msub><h:mi>p</h:mi><h:mi mathvariant="normal">x</h:mi></h:msub></h:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:msub><j:mi>p</j:mi><j:mi mathvariant="normal">y</j:mi></j:msub></j:math> states are involved. As a part of this mixture of states, the band inversion shows no edges in <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mi>k</l:mi></l:math> space. Published by the American Physical Society 2024