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

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

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

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

Quantum Valence Criticality as Origin of Unconventional Critical Phenomena

It is shown that unconventional critical phenomena commonly observed in paramagnetic metals YbRh2Si2, YbRh2(Si0.95Ge0.05)2, and beta-YbAlB4 is naturally explained by the quantum criticality of Yb-valence fluctuations. We construct the mode coupling theory taking account of local correlation effects of f electrons and find that unconventional criticality is caused by the locality of the valence fluctuation mode. We show that measured low-temperature anomalies such as divergence of uniform spin susceptibility \chi T^{-\zeta) with $\zeta~0.6$ giving rise to a huge enhancement of the Wilson ratio and the emergence of T-linear resistivity are explained in a unified way.Comment: 5 pages, 3 figures, to be published in Physical Review Letter

Quantum criticality and emergence of the T/B scaling in strongly correlated metals

A new type of scaling observed in heavy-electron metal β-YbAlB4, where the magnetic susceptibility is expressed as a single scaling function of the ratio of temperature T and magnetic field B over four decades, is examined theoretically. We develop the mode-coupling theory for critical Yb-valence fluctuations under a magnetic field, verifying that the T/B scaling behavior appears near the QCP of the valence transition. Emergence of the T/B scaling indicates the presence of the small characteristic temperature of the critical Yb-valence fluctuation due to the strong local correlation effect. It is discussed that the T/B scaling as well as the unconventional criticality is explained from the viewpoint of the quantum valence criticality in a unified way

Basic Properties of Conductivity and Normal Hall Effect in the Periodic Anderson Model

Exact formulas of diagonal conductivity σxx and Hall conductivity σxy are derived from the Kubo formula in hybridized two-orbital systems with arbitrary band dispersions. On the basis of the theoretical framework for the Fermi liquid based on these formulas, the ground-state properties of the periodic Anderson model with electron correlation and weak impurity scattering are studied on the square lattice. It is shown that imbalance of the mass-renormalization factors causes remarkable increase in σxx and σxy in the valence-fluctuation regime as the f level increases while the cancellation of the renormalization factors causes slight increase in σxx and σxy in the Kondo regime. The Hall coefficient RH shows almost constant behavior in both the regimes. Near half filling, RH is expressed by the total hole density as RH=1/(n¯holee)RH=1/(n¯holee) while RH approaches zero near quarter filling, which reflects the curvature of the Fermi surface. These results hold as far as the damping rate for f electrons is less than about 10% of the renormalized hybridization gap. From these results we discuss pressure dependence of residual resistivity and normal Hall effect in Ce- and Yb-based heavy electron systems