To get an insight into a new type of quantum critical phenomena recently
discovered in the quasicrystal Yb15Al34Au51 and approximant
crystal (AC) Yb14Al35Au51 under pressure, we discuss the
property of the crystalline electronic field (CEF) at Yb in the AC and show
that uneven CEF levels at each Yb site can appear because of the Al/Au mixed
sites. Then we construct the minimal model for the electronic state on the AC
by introducing the onsite Coulomb repulsion between the 4f and 5d orbitals at
Yb. Numerical calculation for the ground state shows that the lattice constant
dependence of the Yb valence well explains the recent measurement done by
systematic substitution of elements of Al and Au in the quasicrystal and AC,
where the quasicrystal Yb15Al34Au51 is just located at the point
from where the Yb-valence starts to change drastically. Our calculation
convincingly demonstrates that this is indeed the evidence that this material
is just located at the quantum critical point of the Yb-valence transition.Comment: 12 pages, 8 figures, Invited Paper in the 26th International
Conference on High Pressure Science & Technology (AIRAPT 26