Effects of Crystalline Electronic Field and Onsite Interorbital Interaction in Yb-based Quasicrystal and Approximant Crystal

To get an insight into a new type of quantum critical phenomena recently discovered in the quasicrystal Yb$_{15}$Al$_{34}$Au$_{51}$ and approximant crystal (AC) Yb$_{14}$Al$_{35}$Au$_{51}$ 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 Yb$_{15}$Al$_{34}$Au$_{51}$ 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

Wide Quantum Critical Region of Valence Fluctuations: Origin of Robust Quantum Criticality in Quasicrystal Yb15Al34Au51 under Pressure

The mechanism of the emergence of robust quantum criticality in the heavy-electron quasicrystal Yb15Al34Au51 is analyzed theoretically. By constructing a minimal model for the quasicrystal and its crystalline approximant, which contain concentric shell structures with Yb and Al-Au clusters, we show that a set of quantum critical points of the first-order valence transition of Yb appears as spots in the ground-state phase diagram. Their critical regions overlap each other, giving rise to a wide quantum critical region. This well explains the robust criticality observed in Yb15Al34Au51 under pressure, and predicts the emergence of the common criticality in the crystalline approximant under pressure. The wider critical region in the quasicrystal than that in the crystalline approximant in the T-P phase diagram and the field-induced valence-crossover "region" in the T-H phase diagram are predicted to appear.Comment: 6 pages, 3 figures, conference proceedings based on the talk at SCES2014 constituted of partly published results in section 2 (J. Phys. Soc. Jpn. 83 (2013) 061006) and new results in section 3 as the self-contained for

Charge Transfer Effect under Odd-Parity Crystalline Electric Field: Divergence of Magnetic Toroidal Fluctuation in β\beta-YbAlB4_4

A novel property of the quantum critical heavy fermion superconductor $\beta$-YbAlB$_4$ is revealed theoretically. By analyzing the crystalline electronic field (CEF) on the basis of the hybridization picture, odd parity CEF is shown to exist because of sevenfold configuration of B atoms around Yb, which breaks the local inversion symmetry. This allows onsite admixture of 4f and 5d wavefunctions with a pure imaginary coefficient, giving rise to the magnetic toroidal (MT) degree of freedom. By constructing a realistic minimal model for $\beta$-YbAlB$_4$, we show that onsite 4f-5d Coulomb repulsion drives charge transfer between the 4f and 5d states at Yb, which makes the MT fluctuation as well as the electric dipole fluctuation diverge simultaneously with the critical Yb-valence fluctuation at the quantum critical point of the valence transition.Comment: 5 pages, 3 figure

Sharp Valence Change as Origin of Drastic Change of Fermi Surface and Transport Anomalies in CeRhIn5 under Pressure

The drastic changes of Fermi surfaces as well as transport anomalies near P=Pc~2.35 GPa in CeRhIn5 are explained theoretically from the viewpoint of sharp valence change of Ce. It is pointed out that the key mechanism is the interplay of magnetic order and Ce-valence fluctuations. It is shown that the antiferromagnetic state with "small" Fermi surfaces changes to the paramagnetic state with "large" Fermi surfaces with huge enhancement of effective mass of electrons with keeping finite c-f hybridization. This naturally explains the de Haas-van Alphen measurement and also the transport anomalies of T-linear resistivity emerging simultaneously with the residual resistivity peak at P=Pc in CeRhIn5.Comment: 4 pages, 2 figures, to appear in Journal of Physics: Conference Serie

Competition between crystalline electric field singlet and itinerant states of f electrons

A new kind of phase transition is proposed for lattice fermion systems with simplified f^2 configurations at each site. The free energy of the model is computed in the mean-field approximation for both the itinerant state with the Kondo screening, and a localized state with the crystalline electric field (CEF) singlet at each site. The presence of a first-order phase transition is demonstrated in which the itinerant state changes into the localized state toward lower temperatures. In the half-filled case, the insulating state at high temperatures changes into a metallic state, in marked contrast with the Mott transition in the Hubbard model. For comparison, corresponding states are discussed for the two-impurity Kondo system with f^1 configuration at each site.Comment: 10 pages LaTeX , 2 eps figures Accepted for publication in Z.Phys.