Electronic model for self-assembled hybrid organic/perovskite semiconductors: Reverse band edge electronic states ordering and spin-orbit coupling

Based on density functional theory, the electronic and optical properties of hybrid organic/perovskite crystals are thoroughly investigated. We consider the monocrystalline 4F-PEPI as material model and demonstrate that the optical process is governed by three active Bloch states at the Γ point of the reduced Brillouin zone with a reverse ordering compared to tetrahedrally bonded semiconductors. Giant spin-orbit coupling effects and optical activities are subsequently inferred from symmetry analysis.

Figure 1

Overview of the crystal structure of 4F-PEPI ([pFC${}_6$H${}_5$C${}_2$H${}_4$NH${}_3$]${}_2$PbI${}_4$).

Figure 2

Electronic band structure of 4F-PEPI (a) without and (b) with the spin-orbit coupling interaction calculated by the density functional theory. The energy levels are referenced to the valence band maximum.

Figure 3

Electronic band structure of [C${}_5$H${}_{11}$NH${}_3$]${}_2$PbI${}_4$ (a) without and (b) with the spin-orbit coupling interaction calculated by the density functional theory. The energy levels are referenced to the valence band maximum.

Figure 4

Electronic wave functions of the valence band maximum VBM and the first two excited states CBM1 and CBM2 as represented in the $b{c}^{*}$ plane.

Figure 5

Dependence of the optical strengths $M_{\mathrm{VBM},\mathrm{CBJ}}^2$ of 4F-PEPI on the direction of the light polarization for the VBM-CBM1 (solid line) and VBM-CBM2 (dotted lines) transitions. The value of $M_{\mathrm{VBM},\mathrm{CB}1}^2$ along the $b$ axis is taken as reference both (a) in the $bc$ plane and (b) in the plane perpendicular to the $b$ axis.

Figure 6

Schematic representation of SAHOP electronic band diagram without (${\Delta }_{\mathrm{SO}}=0$, left) and with (${\Delta }_{\mathrm{SO}}\ne 0$, right) the spin-orbit coupling interaction ${\Delta }_{\mathrm{SO}}$. ${\Delta }_{\mathrm{cr}}$ represents the anisotropy of the crystal field. The (a) real and (b) imaginary parts of the complex spinorial components of the CBM1 and CBM2 states are represented for 4F-PEPI (the spin up component is on top of the spin down component). The section plane and color code used for wave function representation are the same as the ones of Fig. 4. The conclusion concerning optical in-plane isotropy (Fig. 5) is not changed by the inclusion of the spin-orbit interaction.