Perovskite solar cells based on hybrid organic-inorganic lead halide materials have attracted immense interest in recent years due to their enhanced power conversion efficiency. However, the toxic lead element and unstable property of the material limit their applications. With first-principles calculations based on density functional theory, we studied a series of ten lead-free perovskite materials made of cesium, tin, and halogen elements, chlorine (Cl), bromine (Br), and iodine (I). We found that the relative concentrations of the halogen atoms determine the crystal structures and the relative stability of the halide perovskites. Chlorine tends to increase the structural stability, while iodine plays the role of reducing the band gaps of the mixed halide perovskites. Considering the stability and the requirement of suitable band gaps, we identify that, among the ten lead-free halide perovskites, CsSnCl2I, CsSnBr2I, CsSnClBrI, CsSnClI2, CsSnBrI2, and CsSnI3 are the appropriate choices for solar cell applications.

We determine the conditions for bound states (E<0) for arbitrary Cartesian dimension d using a shape-independent regularized pseudopotential with scattering length a for two cold particles in a harmonic trap. It is known for d<=3 that the regularized pseudopotential supports one bound state for positive scattering length but does not support bound states for negative scattering length. We find that the usual (d<=3) positive scattering length bound states rule holds for certain higher odd dimensions d=4n+3 (n=0, 1, ...), but the existence of pseudopotential bound states at other odd dimensions requires a negative scattering length. Specifically, bound states are allowed in higher dimensions d=4n+1 (n=1, 2, ...) but they require a negative scattering length, which might suggest a universe in these dimensions might lead to different chemistry than d=3. We derive analytical approximations for bound state (E<0) and scattering (E>0) energies for a harmonic trap perturbed by the pseudopotential in arbitrary dimensions.