Theory for Magnetic Anisotropy of Field-Induced Insulator-to-Metal Transition in Cubic Kondo Insulator YbB_{12}

Magnetization and energy gap of Kondo insulator YbB_{12} are calculated theoretically based on the previously proposed tight-binding model composed of Yb 5d$\epsilon$ and 4f $\Gamma_8$ orbitals. It is found that magnetization curves are almost isotropic, naturally expected from the cubic symmetry, but that the gap-closing field has an anisotropy: the gap closes faster for the field in (100) direction than in (110) and (111) directions, in accord with the experiments. This is qualitatively understood by considering the maximal eigenvalues of the total angular momentum operators projected on each direction of the magnetic field. But the numerical calculation based on the band model yields better agreement with the experiment.Comment: 4 pages, 4 figures, to appear in J. Phys. Soc. Jp

Indirect and direct energy gaps in the Kondo semiconductor YbB12

Optical conductivity [$\sigma(\omega)$] of the Kondo semiconductor YbB$_{12}$ has been measured over wide ranges of temperature ($T$=8$-$690 K) and photon energy ($\hbar \omega \geq$ 1.3 meV). The $\sigma(\omega)$ data reveal the entire crossover of YbB$_{12}$ from a metallic electronic structure at high $T$ into a semiconducting one at low $T$. Associated with the gap development in $\sigma(\omega)$, a clear onset is newly found at $\hbar\omega$=15 meV for $T \leq$ 20 K. The onset energy is identified as the gap width of YbB$_{12}$ appearing in $\sigma(\omega)$. This gap in \sigma(\omega)$is interpreted as the indirect gap, which has been predicted in the band model of Kondo semiconductor. On the other hand, the strong mid-infrared (mIR) peak observed in$\sigma(\omega)$ is interpreted as arising from the direct gap. The absorption coefficient around the onset and the mIR peak indeed show characteristic energy dependences expected for indirect and direct optical transitions in conventional semiconductors.Comment: 4 pages, 3 figures, submitted to J. Phys. Soc. Jp

Thermal and Dynamical Properties of the Two-band Hubbard Model Compared with FeSi

We study the two-band Hubbard model introduced by Fu and Doniach as a model for FeSi which is suggested to be a Kondo insulator. Using the self-consistent second-order perturbation theory combined with the local approximation which becomes exact in the limit of infinite dimensions, we calculate the specific heat, the spin susceptibility and the dynamical conductivity and point out that the reduction of the energy gap due to correlation is not significant in contrast to the previous calculation. It is also demonstrated that the gap at low temperatures in the optical conductivity is filled up at a rather low temperature than the gap size, which is consistent with the experiment.Comment: 6 pages, LaTeX, 7 PS figures included, uses RevTe

Calculation of Optical Conductivity, Resistivity and Thermopower of Filled Skutterudite CeRu4_4Sb12_{12} based on a Realistic Tight-binding Model with Strong Correlation

The filled-skutterudite compound CeRu$_4$Sb$_{12}$ shows a pseudo-gap structure in the optical conductivity spectra similar to the Kondo insulators, but metallic behavior below 80 K. The resistivity shows a large peak at 80 K, and the Seebeck coefficient is positive and also shows a large peak at nearly the same temperature. In order to explain all these features, a simplified tight-binding model, which captures the essential features of the band calculation, is proposed. Using this model and introducing the correlation effect within the framework of the dynamical mean field approximation and the iterative perturbation theory, the temperature dependences of the optical conductivity, resistivity and the Seebeck coefficient are calculated, which can explain the experiments.Comment: 4 pages, 6 figure

Interplay of Spin-Orbit Interaction and Electron Correlation on the Van Vleck Susceptibility in Transition Metal Compounds

We have studied the effects of electron correlation on Van Vleck susceptibility ($\chi_{\rm{VV}}$) in transition metal compounds. A typical crossover behavior is found for the correlation effect on $\chi_{\rm{VV}}$ as sweeping spin-orbit interaction, $\lambda$. For a small $\lambda$, orbital fluctuation plays a dominant role in the correlation enhancement of $\chi_{\rm{VV}}$; however, the enhancement rate is rather small. In contrast, for an intermediate $\lambda$, $\chi_{\rm{VV}}$ shows a substantial increase, accompanied by the development of spin fluctuation. We will discuss the behavior of $\chi_{\rm{VV}}$ in association with the results of Knight-shift experiments on Sr$_2$RuO$_4$ and an anomalously large magnetic susceptibility observed for $5d$ Ir compounds.Comment: 5 pages, 3 figures, to appear in J. Phys. Soc. Jp

Field-induced phase transitions in a Kondo insulator

We study the magnetic-field effect on a Kondo insulator by exploiting the periodic Anderson model with the Zeeman term. The analysis using dynamical mean field theory combined with quantum Monte Carlo simulations determines the detailed phase diagram at finite temperatures. At low temperatures, the magnetic field drives the Kondo insulator to a transverse antiferromagnetic phase, which further enters a polarized metallic phase at higher fields. The antiferromagnetic transition temperature $T_c$ takes a maximum when the Zeeman energy is nearly equal to the quasi-particle gap. In the paramagnetic phase above $T_c$, we find that the electron mass gets largest around the field where the quasi-particle gap is closed. It is also shown that the induced moment of conduction electrons changes its direction from antiparallel to parallel to the field.Comment: 7 pages, 6 figure

Periodic Anderson model with degenerate orbitals: linearized dynamical mean field theory approach

We investigate a multi-orbital extension of the periodic Anderson model with particular emphasis on electron correlations including orbital fluctuations. By means of a linearized version of the dynamical mean-field theory, we compute the renormalization factor, the density of states, the spectral gap and the local correlation functions for a given set of the intra- and inter-orbital Coulomb interactions as well as the Hund coupling. It is found that when a certain condition is met for the intra- and inter-orbital interactions for $f$ electrons, orbital fluctuations are enhanced, thereby enlarging the Kondo insulating gap. This effect is suppressed in the presence of the Hund coupling. We also clarify how the Kondo insulator is continuously changed to the Mott insulator when electron correlations among conduction electrons are increased.Comment: 7 pages, 10 figure

Investigation of the Two-Particle-Self-Consistent Theory for the Single-Impurity Anderson Model and an Extension to the Case of Strong Correlation

The two-particle-self-consistent theory is applied to the single-impurity Anderson model. It is found that it cannot reproduce the small energy scale in the strong correlation limit. A modified scheme to overcome this difficulty is proposed by introducing an appropriate vertex correction explicitly. Using the same vertex correction, the self-energy is investigated, and it is found that under certain assumptions it reproduces the result of the modified perturbation theory which interpolates the weak and the strong correlation limits.Comment: 5 pages, 7 figures, submitted to J. Phys. Soc. Jp

Excitonic Bound State in the Extended Anderson Model with c-f Coulomb Interaction

The Anderson model with the Coulomb interaction between the local and conduction electrons is studied in the semiconducting phase. Based on a perturbation theory from the atomic limit, leading contributions for the c-f Coulomb interaction are incorporated as a vertex correction to hybridization. An analytical solution shows that the effective attraction in the intermediate states leads to a bound state localized at the local electron site. Self-consistent equations are constructed as an extension of the non-crossing approximation (NCA) to include the vertex part yielding the bound state. A numerical calculation demonstrates the excitonic bound state inside the semiconducting gap for single-particle excitations, and a discontinuity at the gap edge for magnetic excitations.Comment: 15 pages, 20 figures, submitted to J. Phys. Soc. Jp

Density Matrix Renormalization Group Method for the Random Quantum One-Dimensional Systems - Application to the Random Spin-1/2 Antiferromagnetic Heisenberg Chain -

The density matrix renormalization group method is generalized to one dimensional random systems. Using this method, the energy gap distribution of the spin-1/2 random antiferromagnetic Heisenberg chain is calculated. The results are consistent with the predictions of the renormalization group theory demonstrating the effectiveness of the present method in random systems. The possible application of the present method to other random systems is discussed.Comment: 13 pages, 3 figures upon reques