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The extended charge carrier lifetime in hybrid halide perovskites was attributed to a quasi-indirect band gap that arises due to a Rashba splitting in both conduction and valence band edges. In this paper, we present results for an effective relativistic band structure of (CH3NH3)PbI3 with the focus on the dispersion of electronic states near the band edges of (CH3NH3)PbI3 affected by thermal structural fluctuations. We establish a relationship between the magnitude of the Rashba splitting and a deviation of Pb-atom from its centrosymmetric site position in the PbI6 octahedron. For the splitting energy to reach the thermal energy kBT ≈ 26 meV (room temperature), the displacement should be of the order of 0.3Å, which is far above the static displacements of Pb-atoms in the tetragonal phase of (CH3NH3)PbI3. The significant dynamic enhancement of the Rashba splitting observed at earlier simulation times (less than 2 ps) later weakens and becomes less than the thermal energy despite the average displacement of Pb-atoms remaining large (0.37Å). A randomization of Pb-displacement vectors and associated cancelation of the net effective magnetic field acting on electrons at the conduction band edge is responsible for reduction of the Rashba splitting. The lattice dynamics also leads to deterioration of a Bloch character for states in the valence band leading to the subsequent localization of holes, which affects the bipolar mobility of charge carriers in (CH3NH3)PbI3. These results call into question the quasi-indirect band gap as a reason for the long carrier lifetime observed in (CH3NH3)PbI3 at room temperature. Analysis of spin projections and the spin overlap at the band edges also rules out the spin helicity as a possible cause for a long lifetime of optical excitations in perovskite structures. An alternative mechanism involves dynamic localization of holes and their reduced overlap with electrons in reciprocal space.

Due to the presence of heavy elements and the dynamic nature of hybrid halide perovskites, the strong spin–orbit coupling effect can give rise to Rashba band splitting in these materials. Despite many reports on the Rashba effect in 3D perovskites like CH3NH3PbI3, little is known about its presence in two-dimensional Ruddlesden–Popper (2DRP) perovskites. In this work, we use first-principle calculations to investigate the magnitude and origin of the Rashba effect in three families of 2DRP perovskites. We demonstrate the correlation between the splitting magnitude and the octahedron distortions. Moreover, different numbers of inorganic layers, spacer cations, and A-site cations have a great influence on the Rashba splitting through different mechanisms. While structures with C6H5C2H4NH3 (PEA) have a significant Rashba splitting only in the monolayer condition, C4H9NH3 (BA) induces large distortion by tilting the CH3NH3 (MA) cations around all octahedrons, giving rise to a larger Rashba splitting with an increasing number of inorganic layers. Our work elucidates the magnitude and origin of the Rashba splitting in 2DRP perovskites and provides guidelines for the manipulation of the Rashba splitting in these materials.

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Calculations have been made for carbon nanotubes containing substitutional nitrogen impurity atoms using ab initio density functional theory. It is found that the distribution of N atoms depends upon the chirality and diameter of the tube. When two nitrogen atoms are introduced into the (5, 5), (6, 6) and (7, 4) tubes, nitrogen atoms prefer to be adjacent to each other along the circumference, while they tend to be far from each other in other carbon nanotubes. As more nitrogen atoms are incorporated, they prefer to be localized, leading to the broken N – N bond and the interstice is formed in the thin tubes. However, for thick tubes, nitrogen atoms tend to distribute uniformly. It is the finding in this work that the high radial stress plays an important role in nitrogen atom distribution for the thin tubes. For thin N -doped tubes, the major contribution to the structural stabilization comes from the radial stress release after the N – N bond is broken.