Density functional calculations are performed for OH-, F- and H-terminated 4H-SiC 10-20 Å diameter clusters to investigate the effect of surface species upon the optical absorption properties. H-termination results in a pronounced size-dependent quantum-confinement in the absorption, whereas F- and OH-terminations exhibit much reduced size dependent absorption due to surface states. Our finding...

Using first-principles calculations, we have systematically studied the quantum size effects of ultrathin Pb(111) films on the adsorption energies and penetration energy barriers of oxygen atoms. For the on-surface adsorption of oxygen atoms at different coverages, all the adsorption energies are found to show bilayer oscillation behaviors. It is also found that the work function of Pb(111) fil...

The current state of the theory of the Fractional Quantum Hall Effect is critically analyzed, especially the generally accepted concept of composite fermions. It is argued that there is no sound theoretical foundation for this concept. A simple one-dimensional model is proposed, which presumably has an energy spectrum similar to that of the FQHE system. —————————————————————

One kind of hierarchical wave functions of Fractional Quantum Hall Effect (FQHE) on the torus are constructed. The multi-component nature of anyon wave functions and the degeneracy of FQHE on the torus are very clear reflected in this kind of wave functions. We also calculate the braid statistics of the quasiparticles in FQHE on the torus and show they fit to the picture of anyons interacting w...

The Landau problem is discussed in two similar but still different non-commutative frameworks. The “standard” one, where the coupling to the gauge field is achieved using Poisson brackets, yields all Landau levels. The “exotic” approach, where the coupling to the gauge field is achieved using the symplectic structure, only yields lowest-Landau level states, as advocated by Peierls and used in t...

Addition formulas for theta functions of arbitrary order are shown and applied to the theoretical understanding of the fractional quantum Hall effect in a multi-layer two-dimensional many-electron system under periodic conditions.

The “Laughlin” picture of the Fractional Quantum Hall effect can be derived using the “exotic” model based on the two-fold centrally-extended planar Galilei group. When coupled to a planar magnetic field of critical strength determined by the extension parameters, the system becomes singular, and “Faddeev-Jackiw” reduction yields the “Chern-Simons” mechanics of Dunne, Jackiw, and Trugenberger. ...

A major obstacle toward a quantitative verification, by comparison to experiment, of the theory of the excitations of the fractional quantum Hall effect has been the lack of a proper understanding of disorder. We circumvent this problem by studying the neutral magneto-roton excitations, whose energy is expected to be largely insensitive to disorder. The calculated energies of the roton at 1/3, ...

The microscopic approach for studying the half-filled state of the fractional quantum Hall effect is based on the idea of proposing a trial Fermi wave function of the Jastrow-Slater form, which is then fully projected onto the lowest Landau level. A simplified starting point is to drop the projection operator and to consider an unprojected wave function. A recent study claims that such a wave f...