Adiabatic transformation as a search tool for new topological insulators: Distorted ternary Li<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>2</mml:mn></mml:msub></mml:math>AgSb-class semiconductors and related compounds

Abstract

We demonstrate that the first-principles based adiabatic continuation approach is a very powerful and efficient tool for constructing topological phase diagrams and locating nontrivial topological insulator materials. Using this technique, we predict that the ternary intermetallic series Li${}_{2}{M}^{\ensuremath{'}}X$, where ${M}^{\ensuremath{'}}=\text{Cu}$, Ag, Au, or Cd and $X=\text{Sb}$, Bi, or Sn, hosts a number of topological insulators with remarkable functional variants and tunability. We also predict that several III-V semimetallic compounds are topologically nontrivial. We construct a topological phase diagram in the parameter space of the atomic numbers of atoms in Li${}_{2}{M}^{\ensuremath{'}}X$ compounds, which places a large number of topological materials presented in this work as well as in earlier studies within a single unified topological framework. Our results demonstrate the efficacy of adiabatic continuation as a useful tool for exploring topologically nontrivial alloying systems and for identifying new topological insulators even when the underlying lattice does not possess inversion symmetry, and the approaches based on parity analysis are not viable.