The Quasiparticle Electronic Structure of Trigonal CaSnO3 and ZnSnO3 Crystals

The electronic structure of trigonal CaSnO3 and ZnSnO3 crystals was obtained taking into account the quasiparticle corrections to the electron energies, found by means of the Green's function. At the first stage, optimization of the atomic coordinates was realized with the minimization of the total-energy functional and components of the stress tensor. The obtained values of the structural parameters of all crystals have shown a good comparison with the results found by other authors. The second stage was devoted to the calculation of the energy eigenvalues and wave functions within the GGA approach. These results were used in the third stage for calculation of the Green's function. The GGA-GW scheme of finding the Green's function, based on the obtained GGA one-particle states, was applied to all crystals. It is established that the fundamental band gaps Eg, calculated within the GGA and GW approaches, are indirect in ilmenite-type CaSnO3 (Γ–ΓF) and ZnSnO3 (Γ–ΓL). All band gaps found by means of the GGA approach are significantly smaller than the corresponding values obtained within the GW approximation. In particular, in ilmenite-type CaSnO3 the indirect gaps are EgGGA  2.92 eV and EgGW  4.54 eV. In ilmenite-type ZnSnO3, they are EgGGA  1.47 eV and EgGW  3.69 eV. In ZnSnO3 with the LiNbO3 type structure, the calculated direct gaps are (ΓΓ) EgGGA  1.20 eV and EgGW  3.57 eV. The values of the band gaps obtained within the quasiparticle GW approximation are well compared with the experiment. A systematic investigation of the band gap dependence on starting approximation to the GW was carried out in case of trigonal CaSnO3. GW calculations based on HSE06 reveal that the amount of exact Hartree-Fock exchange (mixing parameter) of 0.28 leads to reproducing the experimental band gap of ilmenite-type CaSnO3.The quasiparticle energy bands in ilmenite-type CaSnO3 and ZnSnO3 have been found here for the first time.