Supercell studies of the Fermi surface changes in the electron-doped   superconductor LaFeAsO$_{1-x}$F$_x$
  We study the changes in the Fermi surface with electron doping in the LaFeAsO$_{1-x}$F$_x$ superconductors with density-functional supercell calculations using the linearized augmented planewave (LAPW) method. The supercell calculations with explicit F substitution are compared with those obtained from the virtual crystal approximation (VCA) and from a simple rigid band shift. We find significant differences between the supercell results and those obtained from the rigid-band shift with electron doping, although quite remarkably the supercell results are in good agreement with the virtual crystal approximation (VCA) where the nuclear charges of the O atoms are slightly increased to mimic the addition of the extra electrons. With electron doping, the two cylindrical hole pockets along $\Gamma-Z$ shrink in size, and the third hole pocket around $Z$ disappears for an electron doping concentration in excess of about 7-8%, while the two elliptical electron cylinders along $M-A$ expand in size. The spin-orbit coupling does not affect the Fermi surface much except to somewhat reduce the size of the third hole pocket in the undoped case. We find that with the addition of the electrons the antiferromagnetic state becomes energetically less stable as compared to the nonmagnetic state, indicating that the electron doping may provide an extra degree of stability to the formation of the superconducting ground state. 
P. Larson, S. Satpathy