Realization of an elemental solid-state quasicrystal has remained a distant dream so far in spite of extensive work in this direction for almost two decades. Here, we report the discovery of quasiperiodic ordering in a thick layer of elemental Sn grown on icosahedral ($i$)-Al-Pd-Mn. The STM images and the LEED patterns of the Sn layer show specific structural signatures that portray quasiperiodicity but are distinct from the substrate. Photoemission spectroscopy reveals the existence of the pseudogap around the Fermi energy up to the maximal Sn thickness. The structure of the Sn layer is modeled as a novel form of quasicrystalline clathrate on the basis of the following: Firstly, from ab-initio theory, the energy of bulk Sn clathrate quasicrystal is lower than the high temperature metallic $beta$-Sn phase, but higher than the low temperature $alpha$-Sn phase. A comparative study of the free slab energetics shows that surface energy favors clathrate over $alpha$-Sn up to about 4 nm layer thickness, and matches $beta$-Sn for narrow window of slab thickness of 2-3 nm. Secondly, the bulk clathrate exhibits gap opening near Fermi energy, while the free slab form exhibits a pronouced pseudogap, which explains the pseudogap observed in photoemission. Thirdly, the STM images exhibit good agreement with clathrate model. We establish the adlayer-substrate compatibility based on very similar (within 1%) the cage-cage separation in the Sn clathrate and the pseudo-Mackay cluster-cluster separation on the $i$-Al-Pd-Mn surface. Furthermore, the nucleation centers of the Sn adlayer on the substrate are identified and these are shown to be a valid part of the Sn clathrate structure. Thus, based on both experiment and theory, we propose that 4 nm thick Sn adlayer deposited on 5-fold surface of $i$-Al-Pd-Mn substrate is in fact a metastable realization of elemental, clathrate family quasicrystal.
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