Dynamical and structural symmetries for the highest Landau levels on the <Emphasis Type=Italic>AdS</Emphasis><Subscript>2</Subscript>

The aim of the paper is to use the recurrence relations with respect to both indices of the associated Legendre functions for the extraction of the Dirac quantization condition and dynamical symmetry group U(1, 1) corresponding to the highest Landau levels on the hyperbolic plane with uniform magnetic field B. Irreducible representations of the su(2) algebra are obtained by the ladder differential operators which change B by 1/2 unit and mode number by one unit. Two different classes of the irreducible representations of SU(1, 1) with the even and odd boson numbers 2B − 1/2 are extracted for the Bargmann indices 1/4 and 3/4, respectively. Finally, we show that shape invariance symmetry is realized by the ladder operators which shift only the magnetic field B by 1/2 unit.     

Anisotropic distributions of electrical currents in high-<Emphasis Type=Italic>T</Emphasis><Subscript><Emphasis Type=Italic>c</Emphasis></Subscript> grain-boundary junctions

We developed a self-consistent method for the calculation of spatial current distributions in high-T _c grain-boundary junctions. It is found that crystallographic anisotropy of high-T _c superconducting electrodes results in the effects, which previously were not taken into account for interpretations of experimental data. Among them is a significant redistribution of electrical currents in superconducting electrodes in the vicinity of a grain boundary. In particular in the case of [100]-tilt bicrystal junctions, this current redistribution results in a substantial focusing to the top or bottom part of a thickness of the grain boundary, depending on “roof”- or “valley”-type of the grain boundary. This redistribution is accompanied by generation of vortex currents around the grain boundary, which leads to self-biasing of grain-boundary junctions by magnetic field nucleated by these vortex currents. It is shown that twinning or variation of geometrical shape of the high-T _c electrode may also result in intensive redistribution of electrical currents and nucleation of local magnetic fields inside a high-T _c superconducting electrodes.     

Electronic structure and stability of Mg<Subscript>6</Subscript>Ti<Emphasis Type=Italic>M</Emphasis> (<Emphasis Type=Italic>M</Emphasis> = Mg,Al, Zn) and their hydrides

The influence of Al and Zn atoms on the stability of the Mg₇Ti compound and its hydride Mg₇TiH₁₆ has been studied theoretically. The calculations have been carried out in terms of the full-potential linearized augmented plane wave method. It has been demonstrated that the partial substitution of Al or Zn atoms for magnesium atoms leads to a decrease in the stability of the hydride and to an increase in the stability of the intermetallic compound.