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Quasicrystals (QCs) are intermetallic alloys that have excellent long-range order but lack translational symmetry in at least one dimension. The valence band electronic structure near the Fermi energy  E  F  in such materials is of special interest since it has a direct relation to their unusual physical properties. However, the Fermi surface (FS) topology as well as the mechanism of QC structure stabilization are still under debate. Here we report the first observation of the three-dimensional FS and valence band dispersions near  E  F  in decagonal Al 70 Ni 20 Co 10  (d-AlNiCo) QCs using soft X-ray angle-resolved photoemission spectroscopy. We show that the FS, formed by dispersive Al  sp -states, has a multicomponent character due to a large contribution from high-order bands. Moreover, we discover that the magnitude of the gap at the FS related to the interaction with Brillouin zone boundary (Hume–Rothery gap) critically differs for the periodic and quasiperiodic directions.

Fermi states and anisotropy of Brillouin zone scattering in the decagonal Al–Ni–Co quasicrystal