The effects of static (non-thermal) vs. dynamic (thermal) local distortions on band gaps of cubic oxide and halide perovskites

Numerous symmetry-breaking anomalies, e.g., octahedral tilting in cubic oxide SrTiO₃ and halide CsSnI₃ perovskites were traditionally ascribed to thermal motions whose time-average is zero. We point out that for many cubic perovskites, the internal energy U can be lowered due to intrinsic Distortions off Wyckoff Positions (DOWP’s) before the contribution of thermal motion sets in. Such intrinsic DOWP’s do not time-average to zero, representing non-stochastic, bonding-induced static deformations. We studied for a few cubic oxide/halide perovskites the intrinsic DOWP’s by minimizing the DFT internal energy U at T=0 in a supercell constrained to the cubic shape, followed by observing the dynamic behavior from MD equilibration of G=U-TS at finite T. We propose that these intrinsic DOWP’s form the kernel configurations from which thermally excited stochastic distortions seen in MD simulation. As a result, these intrinsic DOWP’s lead to blueshift band gap in cubic oxide/halide perovskites (e.g., SrTiO₃, CsPbI₃) compared to the nominal cubic (Pm-3m) perovskites. After temperature set in, thermal-induced distortions in cubic SrTiO₃ lead to redshift band gap. Interestingly, the intrinsic DOWP’s in cubic SrTiO₃ lead to a development of distinct Γ-Γ direct band gap.