Matrix Orientifolding and Models with Four or Eight Supercharges

The conditions under which matrix orientifolding and supersymmetry transformations commute are known to be stringent. Here we present the cases possessing four or eight supercharges upon ${\bf Z}_3$ orbifolding followed by matrix orientifolding. These cases descend from the matrix models with eight plus eight supercharges. There are fifty in total, which we enumerate.Comment: 17pages; references adde

Properties of nano-graphite ribbons with zigzag edges -- Difference between odd and even legs --

Persistent currents and transport properties are investigated for the nano-graphite ribbons with zigzag shaped edges with paying attention to system length $L$ dependence. It is found that both the persistent current in the isolated ring and the conductance of the system connected to the perfect leads show the remarkable $L$ dependences. In addition, the dependences for the systems with odd legs and those with even legs are different from each other. On the persistent current, the amplitude for the cases with odd legs shows power-low behavior as $L^{-N}$ with $N$ being the number of legs, whereas the maximum of it decreases exponentially for the cases with even legs. The conductance per one spin normalized by $e^2/h$ behaves as follows. In the even legs cases, it decays as $L^{-2}$, whereas it reaches to unity for $L \to \infty$ in the odd legs cases. Thus, the material is shown to have a remarkable property that there is the qualitative difference between the systems with odd legs and those with even legs even in the absence of the electron-electron interaction.Comment: 4 pagaes, 8 figures, LT25 conference proceeding, accepted for publication in Journal of Physics: Conference Serie

Real-Space Imaging of Alternate Localization and Extension of Quasi Two-Dimensional Electronic States at Graphite Surfaces in Magnetic Fields

We measured the local density of states (LDOS) of a quasi two-dimensional (2D) electron system near point defects on a surface of highly oriented pyrolytic graphite (HOPG) with scanning tunneling microscopy and spectroscopy. Differential tunnel conductance images taken at very low temperatures and in high magnetic fields show a clear contrast between localized and extended spatial distributions of the LDOS at the valley and peak energies of the Landau level spectrum, respectively. The localized electronic state has a single circular distribution around the defects with a radius comparable to the magnetic length. The localized LDOS is in good agreement with a spatial distribution of a calculated wave function for a single electron in 2D in a Coulomb potential in magnetic fields.Comment: 4 pages, 4 figure

Localized Distributions of Quasi Two-Dimensional Electronic States near Defects Artificially Created at Graphite Surfaces in Magnetic Fields

We measured the local density of states of a quasi two-dimensional electron system (2DES) near defects, artificially created by Ar-ion sputtering, on surfaces of highly oriented pyrolytic graphite (HOPG) with scanning tunneling spectroscopy (STS) in high magnetic fields. At valley energies of the Landau level spectrum, we found two typical localized distributions of the 2DES depending on the defects. These are new types of distributions which are not observed in the previous STS work at the HOPG surface near a point defect [Y. Niimi \textit{et al}., Phys. Rev. Lett. {\bf 97}, 236804 (2006).]. With increasing energy, we observed gradual transformation from the localized distributions to the extended ones as expected for the integer quantum Hall state. We show that the defect potential depth is responsible for the two localized distributions from comparison with theoretical calculations.Comment: 4 pages, 3 figure