Electric Dipolar Susceptibility of the Anderson-Holstein Model

The temperature dependence of electric dipolar susceptibility \chi_P is discussed on the basis of the Anderson-Holstein model with the use of a numerical renormalization group (NRG) technique. Note that P is related with phonon Green's function D. In order to obtain correct temperature dependence of P at low temperatures, we propose a method to evaluate P through the Dyson equation from charge susceptibility \chi_c calculated by the NRG, in contrast to the direct NRG calculation of D. We find that the irreducible charge susceptibility estimated from \chi_c agree with the perturbation calculation, suggesting that our method works well.Comment: 4 pages, 4 figure

Spectroscopic confirmation of a cluster of galaxies at z=1 in the field of the gravitational lens MG2016+112

We present new optical data on the cluster AX J2019+1127 identified by the X-ray satellite ASCA at z\sim 1 (Hattori et al. 1997). The data suggest the presence of a high-redshift cluster of galaxies responsible for the large separation triple quasar MG2016+112. Our deep photometry reveals an excess of z\sim 1 galaxy candidates, as already suspected by Benitez et al. (1999). Our spectroscopic survey of 44 objects in the field shows an excess of 6 red galaxies securely identified at z \sim 1, with a mean redshift of z =1.005 +/- 0.002. We estimate a velocity dispersion of \sigma = 771 (+430/-160) km s(-1) based on these 6 galaxies and a V-band mass-to-light ratio of 215 (+308/-77) h_50 M/L_sol. Our observations thus confirm the existence of a massive structure acting as the lens, which explains the unusual configuration of the triple quasar. Hence, there is no more need to invoke the existence of a ``dark cluster'' to understand this lens system.Comment: 8 pages, 4 figures, uses aa.cls, accepted to Astronomy and Astrophysics with minor change

Strong-Coupling Theory of Rattling-Induced Superconductivity

In order to clarify the mechanism of the enhancement of superconducting transition temperature $T_{\rm c}$ due to anharmonic local oscillation of a guest ion in a cage composed of host atoms, i.e., {\it rattling}, we analyze the anharmonic Holstein model by applying the Migdal-Eliashberg theory. From the evaluation of the normal-state electron-phonon coupling constant, it is found that the strong coupling state is developed, when the bottom of a potential for the guest ion becomes wide and flat. Then, $T_{\rm c}$ is enhanced with the increase of the anharmonicity in the potential, although $T_{\rm c}$ is rather decreased when the potential becomes a double-well type due to very strong anharmonicity. From these results, we propose a scenario of anharmonicity-controlled strong-coupling tendency for superconductivity induced by rattling. We briefly discuss possible relevance of the present scenario with superconductivity in $\beta$-pyrochlore oxides.Comment: 8 pages, 6 figure

Kondo Effect of a Magnetic Ion Vibrating in a Harmonic Potential

To discuss Kondo effects of a magnetic ion vibrating in the sea of conduction electrons, a generalized Anderson model is derived. The model includes a new channel of hybridization associated with phonon emission or absorption. In the simplest case of the localized electron orbital with the s-wave symmetry, hybridization with p-waves becomes possible. Interesting interplay among the conventional s-wave Kondo effect and the p-wave one and the Yu-Anderson type Kondo effect is found and the ground state phase diagram is determined by using the numerical renormalization group method. Two different types of stable fixed points are identified and the two-channel Kondo fixed points are generically realized on the boundary.Comment: 15 pages, 17 figures, J. Phys. Soc. Jpn. 80 (2011) No.6 to be publishe

Heavy-Electron Formation and Bipolaronic Transition in the Anharmonic Holstein Model

The emergence of the bipolaronic phase and the formation of the heavy-electron state in the anharmonic Holstein model are investigated using the dynamical mean-field theory in combination with the exact diagonalization method. For a weak anharmonicity, it is confirmed that the first-order polaron-bipolaron transition occurs from the observation of a discontinuity in the behavior of several physical quantities. When the anharmonicity is gradually increased, the polaron-bipolaron transition temperature is reduced as well as the critical values of the electron-phonon coupling constant for polaron-bipolaron transition. For a strong anharmonicity, the polaron-bipolaron transition eventually changes to a crossover behavior. The effect of anharmonicity on the formation of the heavy-electron state near the polaron-bipolaron transition and the crossover region is discussed in detail.Comment: 11 pages, 13 figure

Phonon Dynamics and Multipolar Isomorphic Transition in beta-pyrochlore KOs2O6

We investigate with a microscopic model anharmonic K-cation oscillation observed by neutron experiments in beta-pyrochlore superconductor KOs2O6, which also shows a mysterious first-order structural transition at Tp=7.5 K. We have identified a set of microscopic model parameters that successfully reproduce the observed temperature dependence and the superconducting transition temperature. Considering changes in the parameters at Tp, we can explain puzzling experimental results about electron-phonon coupling and neutron data. Our analysis demonstrates that the first-order transition is multipolar transition driven by the octupolar component of K-cation oscillations. The octupole moment does not change the symmetry and is characteristic to noncentrosymmetric K-cation potential.Comment: 5 pages, 4 figures, submitted to J. Phys. Soc. Jp