Electronic States and Superconducting Transition Temperature based on the Tomonaga-Luttinger liquid in Pr2_{2}Ba4_{4}Cu7_{7}O15−δ_{15-\delta}

An NQR experiment revealed superconductivity of Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$ (Pr247) to be realized on CuO double chain layers and suggests possibility of novel one-dimensional(1D) superconductivity. To clarify the nature of the 1D superconductivity, we calculate the band dispersions of Pr247 by using the generalized gradient approximation(GGA). It indicates that Fermi surface of CuO double chains is well described to the electronic structure of a quasi-1D system. Assuming the zigzag Hubbard chain model to be an effective model of the system, we derive tight binding parameters of the model from a fit to the result of GGA. Based on the Tomonaga-Luttinger liquid theory, we estimate transition temperature ($T_c$) of the quasi-1D zigzag Hubbard model from the calculated value of the Luttinger liquid parameter $K_{\rho}$. The result of $T_c$ is consistent with that of experiments in Pr247 and it suggests that the mechanism of the superconductivity is well understood within the concept of the Tomonaga-Luttinger liquid.Comment: 4 pages, 5 figure

Modification of Angular Velocity by Inhomogeneous MRI Growth in Protoplanetary Disks

We have investigated evolution of magneto-rotational instability (MRI) in protoplanetary disks that have radially non-uniform magnetic field such that stable and unstable regions coexist initially, and found that a zone in which the disk gas rotates with a super-Keplerian velocity emerges as a result of the non-uniformly growing MRI turbulence. We have carried out two-dimensional resistive MHD simulations with a shearing box model. We found that if the spatially averaged magnetic Reynolds number, which is determined by widths of the stable and unstable regions in the initial conditions and values of the resistivity, is smaller than unity, the original Keplerian shear flow is transformed to the quasi-steady flow such that more flattened (rigid-rotation in extreme cases) velocity profile emerges locally and the outer part of the profile tends to be super-Keplerian. Angular momentum and mass transfer due to temporally generated MRI turbulence in the initially unstable region is responsible for the transformation. In the local super-Keplerian region, migrations due to aerodynamic gas drag and tidal interaction with disk gas are reversed. The simulation setting corresponds to the regions near the outer and inner edges of a global MRI dead zone in a disk. Therefore, the outer edge of dead zone, as well as the inner edge, would be a favorable site to accumulate dust particles to form planetesimals and retain planetary embryos against type I migration.Comment: 28 pages, 11figures, 1 table, accepted by Ap