8 tance between these subunits and hardly changes these substructure bond lengths themselves. This is why in a cleavage process very coherent As and La terminated surfaces are expected only. conducting: The electron attractive potential of the O ions moving closer to the topmost La sites brings the outermost La 6 s -bands down in energy by about 2 eV compared to its bulk position so that it crosses Fermi level forming a large electron cylinder FS around Γ, see. Fig. 7. This is another case of the strong polarizability of oxygen in transition metal oxide compounds related to the resonant instability of the O 2 − ion. Since the structural subunits are mutually charged, and those charges are separated in the cleavage process, the strong surface relaxations are even enhanced and the surface triple layers now also internally relax mainly due to their change in charging. While the As tetrahedra shrink in z -direction keeping the Fe ions close to their centers, the La tetrahedra remain nearly unchanged, but the O ions move out of their centers by about 0.3 ˚ A. This is related to a strong change of the ionization state of the O ion, while the ionization state of the Fe ions is hardly changed at the surface. Only the topmost As ions change their ionization state strongly as expected due to the missing doping counterpart, and, of course, also like the topmost La ions of the La terminated surface. Both the As and La terminated surfaces develop a 2D surface band structure of in z -direction well confined band states while the bulk band states are dying off be- tween 10 and 8 ˚ A below the surface As sites of an As ter- minated surface and even about 4 ˚ A deeper in the case of an La terminated surface. Both surface band struc- tures develop FSs. For the As terminated surface and compared to bulk these FSs are expanded around Γ and shrunk nearly to zero at M . Not really a surprise, an ad- ditional FS appears of a band of predominantly Fe 3 d$_{z}$ 2 orbital character (which is completely occupied in the bulk). It is another hole FS with a large radius around Γ and, due to its orbital character its wavefunctions are closest to the surface. For the La terminated surface, on the opposite, the FSs around Γ disappear completely for the surface bands while those around M are expanded. However, as a real surprise, a new electron FS around Γ appears with a medium radius, which has La 6 s orbital character. Towards zone boundary the orbital character of this band continuously changes into mainly La 5 d$_{xz}$ and 5 d$_{yz}$ . Compared to the bulk the corresponding states are lowered in energy by about 2 eV by forming a most strong covalent bond with the O neighbor. It is this en- ergy gain which moves the O ion out of the center of the La tetrahedron. These surface band structures must be expected strongly to influence any surface sensitive experimental result. In particular, it seems to us that ARPES results for NdOFeAs 11 (doped with F) as well as of LaOFeAs 12 show tendencies of As terminated surfaces. As Fig. 7 is based on the results for the slab (LaO) 10 (FeAs) 8 , all FSs shown are again twofold degen- erate, and a noticeable splitting is only seen for the sec- ond FS around M due to a small interaction of the sub- surface FeAs triple layers via the next deeper FeAs layers. Note also that the ‘bulk’ FSs of the figure are slightly shrunk around Γ and expanded around M compared to true bulk FSs. This is because the slab (LaO) 10 (FeAs) 8 is still not thick enough for the Fermi level to converge to its bulk value. There would, however, be no change of the character of the results any more for even thicker slabs. The wavefunction of the La surface band is essentially decayed already at the neighboring O layer and there is a barrier for states at Fermi level down to the next Fe layer (about 4 ˚ A wide). This Fe layer still has strongly deformed bands compared to the bulk with no FS around Γ and two quite large hole cylinders around M . Only at the next deeper Fe layer (about 14 ˚ A beneath the crystal surface) the wavefunction of the bulk bands starts off. Hence, the subsurface FeAs triple layer bands of an La terminated surface deviate just in the opposite direction from the bulk compared to the surface FeAs triple layer bands of an As terminated surface: they shrink to zero at Γ and expand substantially around M . In addition a conducting surface La 6 s -band forms a large electron cylinder around Γ. IV. SUMMARY AND CONCLUSIONS Due to the layered structure of the recently discov- ered iron based superconductor materials, their elec- tronic structure is to various degrees quasi-2D, most pro- nounced in LaOFeAs, the material considered in this pa- per. As expected this situation gives rise to a well devel- oped and perpendicular to the crystal surface well local- ized surface band structure which appears to be dramat- ically different from that in the bulk. Closely interrelated with this deviating surface elec- tronic structure are quite strong surface relaxations of the crystal structure, in the considered material most dramatic for the La terminated surface. Numerical struc- ture relaxations reveal that LaOFeAs has quite stiff LaO and FeAs triple layers as structural subunits which are bound together in a much weaker way. As a result, ten- sile stress in z -direction practically only expands the dis- We gratefully acknowledge assistance by U. Nitzsche with the use of computer facilities. We thank A. Koitzsch and J. van den Brink for helpful discussions. Acknowledgments