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Time- and angle-resolved extreme ultraviolet photoemission spectroscopy isused to study the electronic structure dynamics in BaFe$_2$As$_2$ around thehigh-symmetry points $\Gamma$ and $M$. A global oscillation of the Fermi levelat the frequency of the $A_{1g}$(As) phonon mode is observed. It is argued thatthis behavior reflects a modulation of the effective chemical potential in thephotoexcited surface region that arises from the high sensitivity of the bandstructure near the Fermi level to the $A_{1g}$ phonon mode combined with a lowelectron diffusivity perpendicular to the layers. The results establish a novelway to tune the electronic properties of iron pnictides: coherent control ofthe effective chemical potential. The results further suggest that theequilibration time for the effective chemical potential needs to be consideredin the ultrafast electronic structure dynamics of materials with weakinterlayer coupling.

Ultrafast modulation of the chemical potential in BaFe$_2$As$_2$ by coherent phonons