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Electronic structures of doped BaFe$_2$As$_2$ materials: virtual crystal approximation versus super-cell approach

Employing virtual crystal approximation and super-cell methods for doping, we have performed a comparative study of the electronic structures of various doped BaFe$_2$As$_2$ materials by first principles simulations. Both of these methods give rise to a similar density of states and band structures in case of hole doping (K doping in Ba site) and iso-electronic P doping in As site. But in case of electron doped systems with higher doping concentration, electronic structures, calculated using virtual crystal approximation approach deviates from that of the super-cell method. On the other hand in case of iso-electronic Ru doping implemented by virtual crystal approximation, an extra shift of the chemical potential in electronic structure in comparison to super-cell method is observed and that shift can be used to predict the correct electronic structure within virtual crystal approximation as reflected in our calculated Fermi surfaces. But for higher Ru doping concentration, simple shifting of chemical potential does not work as the electronic structure calculated by virtual crystal approximation approach is entirely different from that of the calculated by super-cell formalism.