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We revisit the problem that relevant parts of bandstructures for a given cellchoice can reflect exact or approximate higher symmetries of subsystems in thecell and can therefore be significantly simplified by an unfolding procedurethat recovers the higher symmetry. We show that bandstructure unfolding can beunderstood as projection onto induced irreducible representations of a groupobtained by extending the original group of translations with a number ofadditional symmetry operations. The resulting framework allows us to define ageneralized unfolding procedure which includes the point group operations andcan be applied to any quantity in the reciprocal space. The unfolding of theBrillouin zone follows naturally from the properties of the induced irreduciblerepresentations. In this context, we also introduce a procedure to derivetight-binding models of reduced dimensionality by making use of point groupsymmetries. Further, we show that careful consideration of unfolding hasimportant consequences on the interpretation of angle resolved photoemissionexperiments. Finally, we apply the unfolding procedure to variousrepresentative examples of Fe-based superconductor compounds and show that theone iron picture arises as an irreducible representation of the glide mirrorgroup and we comment on the consequences for the interpretation of one-ironversus two-iron Brillouin zone representations.

Unfolding of the electronic structure through the induced representations of space groups: Application to Fe-based superconductors