  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.
