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Density functional theory study of the electronic structure of fluorite Cu$_{2}$Se

We have investigated the electronic structure of fluorite Cu$_{2}$Se using density functional theory calculations within the LDA, PBE and AM05 approximations as well as with the non-local hybrid PBE0 and HSE approximations. Our results show that Cu$_{2}$Se is a zero gap semiconductor when using either a local or semi-local density functional approximation while there exists a gap when using the PBE0 functional. For the HSE approximation, we find that the presence of a gap depends on the range separation for the non-local exchange within the HSE approximation. For the occupied states we find that the LDA, PBE, AM05, PBE0 and HSE agrees when regarding the overall structure, however, the hybrid functionals are shifted towards lower energy values compared to the LDA, PBE and AM05. The valence bands obtained using the hybrid functionals are in good agreement with experimental valence band spectra. We also find that the PBE, PBE0 and HSE approximations give similar results regarding bulk properties, such as lattice constants and bulk modulus. In addition, we have investigated the localization of the Cu d-states and its effect on the band gap in the material using the LDA+U approach. We find that a gap is opened up by increasing the $U$, however, the $U$ values required for a gap opening is unrealistically high.