Why different boundary conditions get different fermi level?

[395235863]

Why different boundary conditions get different fermi level?
examples are given as pic.1

[Jess Wellendorff]

Changing a boundary condition may shift the electronic eigenvalue spectrum, and therefore also the Fermi level. Look slike you also used different k-point samplings. This will definitely result in a shift of the Fermi level, but may not affect band energy differences much.

[Anders Blom]

And, most importantly, the absolute value of the Fermi level doesn't mean anything, since you don't know the energy zero-point reference. All band structures are always reported relative the Fermi level  and that's typically all that matters.