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 $\mathit{\text{s-p}}$ band inversion at $\gamma$ (V/V${}_0$) = 0.76 and 0.73, respectively. The cubic perovskite shows the surface state at $\bar{M}$, whereas, the pseudocubic structure shows two conducting states in the neighbourhood of $\bar{M}$, 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${}_3$ ($\mathit{\text{x}}$ = 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 $\mathit{\text{initio}}$ molecular dynamics at operational temperature. Their structural stability under compression strengthens the experimental relevance.