Spin–orbit coupling effect on energy level splitting and band structure inversion in CsPbBr3

The band structures and density of states (DOS) of all the three structural configurations of CsPbBr 3 without spin–orbit coupling (SOC = 0) and with the addition of spin–orbit coupling (SOC ≠ 0) effects were calculated, using density functional theory. Upon the inclusion of the spin–orbit coupling, the bandgaps exhibit reductions of 1.27 eV, 1.16 eV and 1.08 eV for the cubic, tetragonal and orthorhombic phases, respectively. These calculations provide a positive split-off energy value of Δ so = 1.69 eV for the simple cubic phase. For the lower symmetry phases, the p -like fourfold degenerate Γ 8 v ( 4 ) band has been observed to split to form two bands, in addition to the Γ 6 v ( 2 ) split-off band. The calculated splitting energies between these bands are found to be in close agreement with previous experimentally measured values. The calculated electronic band structures show that CsPbBr 3 has a negative ‘inversion energy’ (Δ i