Graphene with geometrically induced vorticity

At half filling, the electronic structure of graphene can be modeled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field an everywhere-real Kekulé modulation of the hopping matrix elements can correspond to a nonreal Higgs field with nontrivial vorticity. This provides a natural setting for fractionally charged vortices with localized zero modes. For fullerenelike molecules we employ the index theorem to demonstrate the existence of six low-lying states that do not depend strongly on the Kekulé-induced mass gap

Zero modes of various graphene confiurations from the index theorem

In this article we consider a graphene sheet that is folded in various compact geometries with arbitrary topology described by a certain genus, g. While the Hamiltonian of these systems is defined on a lattice one can take the continuous limit. The obtained Dirac-like Hamiltonian describes well the low energy modes of the initial system. Starting from first principles we derive an index theorem that corresponds to this Hamiltonian. This theorem relates the zero energy modes of the graphene sheet with the topology of the compact lattice. For g = 0 and g = 1 these results coincide with the analytical and numerical studies performed for fullerene molecules and carbon nanotubes while for higher values of g they give predictions for more complicated molecules

Formation of an Edge Striped Phase in Fractional Quantum Hall Systems

We have performed an exact diagonalization study of up to N=12 interacting electrons on a disk at filling $\nu={1/3}$ for both Coulomb and $V_1$ short-range interaction for which Laughlin wave function is the exact solution. For Coulomb interaction and $N\geq 10$ we find persistent radial oscillations in electron density, which are not captured by the Laughlin wave function. Our results srongly suggest formation of a chiral edge striped phase in quantum Hall systems. The amplitude of the charge density oscillations decays slowly, perhaps as a square root of the distance from the edge; thus the spectrum of edge excitations is likely to be affected.Comment: 4 pages, 3 Figs. include

Interlayer Exchange Interactions, SU(4) Soft Waves and Skyrmions in Bilayer Quantum Hall Ferromagnets

The Coulomb exchange interaction is the driving force for quantum coherence in quantum Hall systems. We construct a microscopic Landau-site Hamiltonian for the exchange interaction in bilayer quantum Hall ferromagnets, which is characterized by the SU(4) isospin structure. By taking a continuous limit, the Hamiltonian gives rise to the SU(4) nonlinear sigma model in the von-Neumann-lattice formulation. The ground-state energy is evaluated at filling factors $\nu =1,2,3,4$. It is shown at $\nu =1$ that there are 3 independent soft waves, where only one soft wave is responsible for the coherent tunneling of electrons between the two layers. It is also shown at $\nu =1$ that there are 3 independent skyrmion states apart from the translational degree of freedom. They are CP$^{3}$ skyrmions enjoying the spin-charge entanglement confined within the \LLL.Comment: 12 pages, 2 figure

Composite Fermion Description of Correlated Electrons in Quantum Dots: Low Zeeman Energy Limit

We study the applicability of composite fermion theory to electrons in two-dimensional parabolically-confined quantum dots in a strong perpendicular magnetic field in the limit of low Zeeman energy. The non-interacting composite fermion spectrum correctly specifies the primary features of this system. Additional features are relatively small, indicating that the residual interaction between the composite fermions is weak. \footnote{Published in Phys. Rev. B {\bf 52}, 2798 (1995).}Comment: 15 pages, 7 postscript figure

Universal structure of the edge states of the fractional quantum Hall states

We present an effective theory for the bulk fractional quantum Hall states on the Jain sequences on closed surfaces and show that it has a universal form whose structure does not change from fraction to fraction. The structure of this effective theory follows from the condition of global consistency of the flux attachment transformation on closed surfaces. We derive the theory of the edge states on a disk that follows naturally from this globally consistent theory on a torus. We find that, for a fully polarized two-dimensional electron gas, the edge states for all the Jain filling fractions $\nu=p/(2np+1)$ have only one propagating edge field that carries both energy and charge, and two non-propagating edge fields of topological origin that are responsible for the statistics of the excitations. Explicit results are derived for the electron and quasiparticle operators and for their propagators at the edge. We show that these operators create states with the correct charge and statistics. It is found that the tunneling density of states for all the Jain states scales with frequency as $|\omega|^{(1-\nu)/\nu}$.Comment: 10 page

Remote site control of an active site fidelity checkpoint in a viral RNA-dependent RNA polymerase

The kinetic, thermodynamic, and structural basis for fidelity of nucleic acid polymerases remains controversial. An understanding of viral RNA-dependent RNA polymerase (RdRp) fidelity has become a topic of considerable interest as a result of recent experiments that show that a 2-fold increase in fidelity attenuates viral pathogenesis and a 2-fold decrease in fidelity reduces viral fitness. Here we show that a conformational change step preceding phosphoryl transfer is a key fidelity checkpoint for the poliovirus RdRp (3D pol). We provide evidence that this conformational change step is orientation of the triphosphate into a conformation suitable for catalysis, suggesting a kinetic and structural model for RdRp fidelity that can be extrapolated to other classes of nucleic acid polymerases. Finally, we show that a site remote from the catalytic center can control this checkpoint, which occurs at the active site. Importantly, similar connections between a remote site and the active site exist in a wide variety of viral RdRps. The capacity for sites remote from the catalytic center to alter fidelity suggests new possibilities for targeting the viral RdRp for antiviral drug development. © 2005 by The American Society for Biochemistry and Molecular Biology, Inc

Bulk Versus Edge in the Quantum Hall Effect

The manifestation of the bulk quantum Hall effect on edge is the chiral anomaly. The chiral anomaly {\it is} the underlying principle of the ``edge approach'' of quantum Hall effect. In that approach, \sxy should not be taken as the conductance derived from the space-local current-current correlation function of the pure one-dimensional edge problem.Comment: 4 pages, RevTex, 1 postscript figur

Quantum dots in high magnetic fields: Rotating-Wigner-molecule versus composite-fermion approach

Exact diagonalization results are reported for the lowest rotational band of N=6 electrons in strong magnetic fields in the range of high angular momenta 70 <= L <= 140 (covering the corresponding range of fractional filling factors 1/5 >= nu >= 1/9). A detailed comparison of energetic, spectral, and transport properties (specifically, magic angular momenta, radial electron densities, occupation number distributions, overlaps and total energies, and exponents of current-voltage power law) shows that the recently discovered rotating-electron-molecule wave functions [Phys. Rev. B 66, 115315 (2002)] provide a superior description compared to the composite-fermion/Jastrow-Laughlin ones.Comment: Extensive clarifications were added (see new footnotes) regarding the difference between the rotating Wigner molecule and the bulk Wigner crystal; also regarding the influence of an external confining potential. 12 pages. Revtex4 with 6 EPS figures and 5 tables . For related papers, see http://www.prism.gatech.edu/~ph274c