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

Comment on ``Effective Mass and g-Factor of Four Flux Quanta Composite Fermions"

In a recent Letter, Yeh et al.[Phys. Rev. Lett. 82, 592 (1999)] have shown beautiful experimental results which indicate that the composite fermions with four flux quanta ($^4$CF) behave as fermions with mass and spin just like those with two flux quanta. They observed the collapse of the fractional quantum Hall gaps when the following condition is satisfied with some integer $j$, $g^*\mu_{\rm B}B_{\rm tot} = j \hbar \omega_{\rm c}^*$, where $g^*$ and $\omega_{\rm c}^*$ are the g-factor and the cyclotron frequency of the $^4$CF, respectively. However, in their picture the gap at the Fermi energy remains always finite even if the above condition is satisfied, thus the reason of the collapse was left as a mystery. In this comment it is shown that part of the mystery is resolved by considering the electron-hole symmetry properly.Comment: 2 pages, RevTeX. Minor chang

On transport in quantum Hall systems with constrictions

Motivated by recent experimental findings, we study transport in a simple phenomenological model of a quantum Hall edge system with a gate-voltage controlled constriction lowering the local filling factor. The current backscattered from the constriction is seen to arise from the matching of the properties of the edge-current excitations in the constriction ($\nu_{2}$) and bulk ($\nu_{1}$) regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model, finding that a competition between two tunneling process, related by a quasiparticle-quasihole symmetry, determines the fate of the low-bias transmission conductance. In this way, we find satisfactory explanations for many recent puzzling experimental results.Comment: 4 pages, 4 figure

Density Matrix Renormalization Group and the Nuclear Shell Model

We describe the use of the Density Matrix Renormalization Group method as a means of approximately solving large-scale nuclear shell-model problems. We focus on an angular-momentum-conserving variant of the method and report test results for the nucleus $^{48}Cr$. The calculation is able to reproduce both the ground state energy and the energy of the first excited state, by diagonalizing matrices much smaller than those of the full shell model.Comment: 7 pages, 3 figures; To appears in Phys. Rev.