Strain-driven topological quantum phase transition in the family of halide perovskites

The centrosymmetric halide perovskites undergo a continuous phase transition from a normal insulator to a topological insulator at the critical value of strain. Contrarily, in noncentrosymmetric halide perovskites, this phase transition is discontinuous. The noncentrosymmetry does not stabilize the gapless state, causing a discontinuity in the bandgap. We have employed the density functional theory and Slater-Koster formalism-based tight-binding Hamiltonian studies to understand the evolution of band topology under the compressive strain in the halide perovskites. Our study shows that both cubic and pseudocubic FAPbI$_3$ undergo a Pb $\textit{s-p}$ band inversion at $\gamma$ (V/V$_0$) = 0.76 and 0.73, respectively. The cubic perovskite shows the surface state at $\overline{M}$, whereas, the pseudocubic structure shows two conducting states in the neighbourhood of $\overline{M}$, unlike the conventional topological insulator. The Pb-Pb second nearest neighbor interactions determine this topological phase transition. Alongside, we have modeled mixed cation halide perovskites Cs$_x$MA$_{1-x}$PbI$_3$ (\textit{x} = 0.25, 0.5 and 0.75) to study their topological properties. Cs$_{0.5}$MA$_{0.5}$PbI$_3$ shows non-trivial topology at $\gamma$ = 0.74. In addition, we have checked the structural stability of different strained configurations using ab \textit{initio} molecular dynamics at operational temperature. Their structural stability under compression strengthens the experimental relevance.