Antiferroelectric Topological Insulators in Orthorhombic $A\mathrm{MgBi}$ Compounds ($A=\mathrm{Li}$, Na, K)

We introduce antiferroelectric topological insulators as a new class of functional materials in which an electric field can be used to control topological order and induce topological phase transitions. Using first principles methods, we predict that several alkali-MgBi orthorhombic members of an $ABC$ family of compounds are antiferroelectric topological insulators. We also show that epitaxial strain and hydrostatic pressure can be used to tune the topological order and the band gap of these $ABC$ compounds. Antiferroelectric topological insulators could enable precise control of topology using electric fields, enhancing the applicability of topological materials in electronics and spintronics.

Figure 1

Schematic representation of (a) a ferroelectric topological insulator and (b) an antiferroelectric topological insulator with an antipolar normal insulator (NI) state and two polar topological insulator (TI) states, referred to as a type I antiferroelectric topological insulator in the text.

Figure 2

Band gap of the LiMgBi compound of polar $P{6}_{3}mc$ (top) and antipolar $Pnma$ (bottom) structures as a function of epitaxial strain, calculated using the LDA functional. The $P{6}_{3}mc$ structure exhibits regions in which it is a topological insulator (TI), a Weyl semimetal (WSM), and a normal insulator (NI), whereas the $Pnma$ structure exhibits metallic and normal insulator phases. Note that the $Pnma$ structure at zero strain is distinct from the equilibrium $Pnma$ structure due to the $\sqrt{3}$ ratio that the in-plane lattice parameters must obey.

Figure 3

Band structure of LiMgBi in the polar $P{6}_{3}mc$ structure at strains of $-2.9\%$ (left) corresponding to a normal insulator, and $+0.3\%$ (right) corresponding to a topological insulator.

Figure 4

Band gap of the KMgBi compound of polar $P{6}_{3}mc$ (top) and antipolar $Pnma$ (bottom) structures as a function of hydrostatic pressure calculated using the LDA functional. The $P{6}_{3}mc$ structure exhibits a topological insulator (TI) regime and a metallic regime, whereas the $Pnma$ structure exhibits topological insulator and normal insulator (NI) phases.