The Fermi surfaces (FS) of LaOFeAs (in $k_z$=0 plane) consist of two hole-type circles around $Gamma$ point, which do not touch each other, and two electron-type co-centered ellipses around M point, which are degenerate along the M-X line. By first-principles calculations, here we show that additional degeneracy exists for the two electron-type FS, and the crucial role of F-doping and pressure is to enhance this orbital degeneracy. It is suggested that the inter-orbital fluctuation is the key point to understand the unconventional superconductivity in these materials.
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