Physical properties of bulk, defective, 2D and 0D metal halide perovskite semiconductors from a symmetry perspective

Metal halide perovskite-based nanostructures, nanosheets and nanoparticles at the forefront, show attractive optoelectronic properties, suitable for photovoltaics and light emission applications. Achieving a sounded understanding of these basic electronic and optical properties represents therefore a crucial step for the full technological exploitation of this class of semiconductors. The rapidly expanding chemical engineering and their unusual structural diversity is fascinating but also challenging for a rational description on par with those well-known for conventional semiconductors. In this sense, group theory-based symmetry analyses offer a general and rigorous approach to understand the properties of various bulk perovskites and perovskite-based nanostructures. In this work, we review the electronic and optical response of metal halide perovskite semiconductors using symmetry analysis from group theory, recalling the main results for the prototypical cubic Pm-3m lattice of AMX(3)bulk perovskites (where A is cation, M metal and X halide), then extending the analysis to three cases of technological interest: AMX(3)nanoparticles, A(4)MX(6)isolated octahedra, A(2)MX(4)layered systems, and recently introduced deficient halide perovskites (d-HP). On the basis of symmetry arguments, we will stress analogies and differences in the electronic and optical properties of these materials, as induced by the spatial confinement and dimensionality. Meanwhile, we will take advantage of this analysis to discuss recent results and debates from the literature, as the energetics of dark/bright states in the band-edge exciton fine structure of perovskite nanoparticles and nanosheets. From the present work, we also anticipate that the band-edge exciton fine structure of d-HP does not present optically dark states, in striking contrast to AMX(3)nanoparticles and layered perovskites, a fact that can have important consequences on the photophysics of these novel perovskitoids.