Theoretical investigation of self-trapped hole (STH) polarons in cubic and rhombohedral phases of NaNbO3

Abstract

In this study we investigate the formation of the self-trapped hole (STH) in two high and low-temperature phases of $\mathrm{NaNbO_{3}}$ (cubic and rhombohedral phases) by using both DFT with application of local potentials and HSE06. In both phases, we first investigate the existence of polaron in the lattice which is manually distorted and one electron is removed from its system. Then various energy regimes of formed STH is calculated using DFT+U and HSE06 in order to investigate the stability of the formed STH. Comparing trapping energy of STH in rhombohedral and cubic phase shows that the appeared STH in rhombohedral phase of $\mathrm{NaNbO_{3}}$ is noticeably more stable compared to the one in cubic phase in condition which U parameter applied on Nb and O atoms in both cases are equal. It is then shown that applying various U parameters on Nb and O atoms, yield a piecewise linear behaviour of the total energy with respect to fractional charge. In order to find the best U parameter which can be used for future works, lattice parameters and band gap obtained from different composition of U parameter on Nb and O are compared to the available experimental results. In the case of rhombohedral phase, U(Nb4d)= 4,6 eV and U(O2p)= 4 eV gives a very good linear response in total energy curves with respect to fractional charge and have a good agreement with experimental data. For cubic phase, U(Nb4d)= 4 eV and U(O2p)= 6 eV is in best agreement with experimental studies.