Fig. 4: Electronic and optical properties of bulk and 2D CH₃NH₃PbBr₃.

a, b DFT calculated band structures together with their respective Brillouin zone (BZ), see insets, for bulk and n = 0 (green), 3 (gray), respectively. Symmetry points at boundaries of the BZ zone where the direct bandgap changes from the R (in bulk) to the M (in n = 0, 3) point. k_z is oriented in parallel to the out-of-plane (OP) direction while k_x and k_x along of the in-plane (IP) direction. The valence band maximum (VBM) and conduction band minimum (CBM) are highlighted via the open and filled circles, respectively. The arrows correspond to the first optical transitions in both systems. c, d, e Show the iso-surfaces (±0.0016 e Å⁻³ for n-layer and ±0.0003 e Å⁻³ for bulk) of the charge densities at VBM and CBM for bulk, n = 0, and n = 3, respectively. The orientation of the supercells in terms of OP and IP coordinates is shown in d. f G₀W₀-BSE calculated optical absorption for n = 0 with IP (green) and OP (blue) polarizations including the oscillator strengths for the main excitations: A, B, and C. The difference in energy range observed between n = 0 and n = 3 (Fig. 3a) is due to the strong confinement for the former. g G₀W₀ quasi-particles (QP) eigenstates (dots) calculated for n = 0 along Γ-X-M. Occupied (empty) states are below (above) 0 eV. The eigenstates that contribute to excitations A, B, and C are displayed in blue, green, and red, respectively. The size of the circles is proportional to the weight of the states composing a given excitation. For instance, excitation A has a strong contribution from transitions from VBM to CBM at M, as well as several minor transitions along of X to M. Excitations B and C follow similar analysis. Note that the supercell coordinates (x, y, z) used here is physically different from those in radiation patterns (Fig. 1). All simulations include vdW interactions.