Mott transition and heavy fermion state in the pyrochlore Hubbard model

We investigate the interplay between geometrical frustration and strong electron correlation based upon the pyrochlore Hubbard model. In the half-filling case, using the perturbative expansion in terms of electron correlation, we show that the self-energy shows a divergent behavior leading the system into the Mott insulating state, in which quantum disordered spin liquid without magnetic long-range order realizes. In the hole-doped case, we obtain heavy-fermion-like Fermi liquid state. We also calculate the neutron cross section which is well consistent with recent neutron scattering experiments for itinerant pyrochlore systems.Comment: 5 pages, 5 figures, revised version accepted for the publication in Phys. Rev.

Metal-to-Insulator Transition, Spin Gap Generation, and Charge Ordering in Geometrically Frustrated Electron Systems

We investigate a (semi-)metal to insulator transition (MIT) realized in geometrically frustrated electron systems on the basis of the Hubbard model on a three-dimensional pyrochlore lattice and a two-dimensional checkerboard lattice. Using the renormalization group method and mean field analysis, we show that in the half-filling case, MIT occurs as a result of the interplay between geometrical frustration and electron correlation. In the insulating phase, which has a spin gap, the spin rotational symmetry is not broken, while charge ordering exists. The charge ordered state is stabilized so as to relax the geometrical frustration in the spin degrees of freedom. We also discuss the distortion of the lattice structure caused by the charge ordering. The results are successfully applied to the description of the MIT observed in the pyrochlore system ${\rm Tl_2Ru_2O_7}$.Comment: 12 pages, 10 figure

Giant Nernst and Hall Effects in Chiral Superconductors due to Berry Phase Fluctuations

We consider the Nernst and Hall effects in fluctuation regime of chiral superconductors above transition temperatures, that are raised not by conventional Lorentz force, but by asymmetric scattering due to fluctuations of the Berry phase of the Bogoliubov-de Gennes Hamiltonian. It is found that these effects can be more significant than conventional ones for cleaner samples, exhibiting qualitatively distinct behaviors. The results provide systematic and comprehensive understanding for recent experimental observations of the Nernst effect in a clean URu$_2$Si$_2$ sample, which is suggested to be a chiral superconductor