Anomalous Behavior in Dark-Bright Splitting Impacts the Biexciton Binding Energy in (BA)₂(MA)_n-1Pb_nBr_{3 n+1} (n = 1-3)

Two-dimensional Ruddlesden-Popper series are an excellent system for tuning physical properties of the perovskite by controlling the layer number (n). For instance, bandgap and exciton binding energies of the series gradually increase upon reducing n via enhanced quantum and dielectric confinements. Here, we present findings that challenge the anticipated trend in electron-hole exchange interaction within (BA)₂MA_n-1Pb_nBr_3n+1 (n = 1-3), which causes spin-dependent exciton level splitting into bright and dark states, where the latter is partially visible near the surface of the Br-based two-dimensional Ruddlesden-Popper series. Contrary to expectations, the smallest gap between bright and dark exciton levels is observed from n = 2 at 10 K. This anomaly results in the strongest biexciton binding between two dark excitons occurring at n = 2, rather than at n = 1 as initially hypothesized. The observed anomaly arises from a phase transition induced by octahedral tilting occurring only for n = 2 near 100 K as confirmed by temperature-dependent optical and X-ray diffraction measurements. Our results show that Coulomb interaction need not vary gradually with n, which can impact the optoelectronic properties of the Ruddlesden-Popper series.