Electronic structures of lead iodide based low-dimensional crystals

The electronic structures of three-dimensional and two-dimensional lead-halide-based crystals ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ and $({\mathrm{C}}_4{\mathrm{H}}_9{\mathrm{NH}}_3{)}_2{\mathrm{PbI}}_4$ are investigated by photoelectron spectroscopy and band calculations using the linear combination of atomic orbitals within the density-functional theory. For both crystals, the top of the valence band is found to consist mainly of the $\sigma$-antibonding states of Pb $6s$ and I $5p$ orbitals, and the bottom of the conduction band to be composed primarily of the $\sigma$-antibonding states of Pb $6p$ and I $5s$ orbitals. Photoelectron spectra of the valence-band region indicate that the electronic structures change depending on the dimensionality of the crystals. Based on the calculation results, the differences observed in the spectra are rationalized in terms of narrowing bandwidth as the dimensionality decreases from three to two dimensions. It is shown that the bandwidth narrowing of the two-dimensional crystal is due to zero dispersion in the vertical direction and the Jahn-Teller effect in the layered structure. These effects lead to a wideband gap and high exciton stability in $({\mathrm{C}}_4{\mathrm{H}}_9{\mathrm{NH}}_3{)}_2{\mathrm{PbI}}_4.$