Hybrid Improper Ferroelectricity and Moir\'e Superlattices-induced Exciton Quantization in Layered 2D Halide Perovskite

2D Ruddlesden-Popper perovskites are compelling platforms for quantum-confined optoelectronics. However, polar order in iodide composition remains rare under ambient conditions, and the mechanistic origin of anomalous photoluminescence in this class of perovskite is still speculative. Here, we demonstrate that solution-grown $(PA)_2FAPb_2I_7$ single crystals develop an inadvertent moir\'e superlattice through pseudo-merohedral twinning, driven by hybrid improper ferroelectricity in which trilinear mode coupling between two primary zone-boundary modes ($X_2^+$ and $X_3^-$) and a secondary $\Gamma_4^-$ polar displacement simultaneously breaks inversion symmetry and imposes a ca. 5.17{\deg} rotational misalignment between adjacent layers. This symmetry breaking activates one of the highest piezoelectric coefficients $d_{33}$ (ca. 20 pm/V) reported among 2D perovskites. This misalignment generates a moir\'e superlattice that undergoes a thermally driven commensurate-incommensurate transition, switching between a periodic confinement potential that quantizes excitons into an equidistant photoluminescence ladder at 123 K and a disordered incommensurate phase with broadened emission at 298 K. These emissions are attributed to moir\'e-confined excitons, resolving a longstanding debate on anomalous secondary photoluminescence in layered 2D perovskites and opening pathways to twistronics, photoferroelectrics and piezo-optoelectronic devices.