Tunneling state anisotropy in a single grain decagonal quasicrystal.

We present low-temperature measurements, between 20 mK and 20 K, of the sound velocity variations in a single grain of the decagonal quasicrystal Al-Ni-Co. We have used acoustic shear waves of frequency 70 MHz propagating in the quasicrystalline planes with two different polarizations: parallel and perpendicular to the quasicrystalline planes. Our results show the presence of tunneling states (TSs) with a strong difference of the phonon-TS coupling for the two polarizations, which reveals a strong anisotropy of distribution of the orientations of the TSs in the sample. This result gives direct evidence that TSs are generated by the quasicrystalline structure itself.