I want to know why we need fake k-points in HSE band structure calculation? I mean why we can't take a simple high symmetric path like we do in PBE calculation?
The reason is that the HSE method are obtaining the band structure with self-consistent calculation rather than non-self-consistent calculation like PBE band structure calculation. For self-consistent calculation, you will sample the k-space with a uniform k mesh. The fake k-points are just the high-symmetry path used in PBE calculations, which are added into the self-consistent calculations to calculate the eigenvalues or energy band you are wanted.
This question has already been answered in the quantum espresso forum here. To reiterate the Fock operator at a certain k-point needs the wavefunction on a grid that is commensurate with it. Hence we cannot calculate the single k-point non-selfconsistently from the charge density. Therefore, in a hybrid functional we have to use the entire self consistent calculations.