A recently developed model of interacting composite fermions, is used to investigate different composite-fermion phases. Their interaction potential allows for the formation of both solid and new quantum-liquid phases, which are interpreted in terms of second-generation composite fermions and which may be responsible for the fractional quantum Hall states observed at unusual filling factors, su...

We review our recent theoretical works on the the quantum spin Hall effect. First we compare edge states in various 2D systems, and see whether they are robust or fragile against perturbations. Through the comparisons we see the robust nature of edge states in 2D quantum spin Hall phases. We see how it is protected by the Z2 topological number, and reveal the nature of the Z2 topological number...

We present a Chern-Simons theory of the fractional quantum Hall effect in which flux attachment is followed by a transformation that effectively attaches the correlation holes. We extract the correlated wave functions, compute the drift and cyclotron currents (due to inhomogeneous density), exhibit the Read operator and operators that create quasiparticles and quasiholes. We show how the bare k...

The effect of the complex valence-band Landau-level ~LL! structure on the fractional quantum Hall ~FQH! effect of a two-dimensional hole system has been studied in a modulation-doped quantum well ~QW! with front and back gates. Owing to the spin-orbit interaction and the band mixing in the valence band, changing the potential asymmetry of the QW with the front and back gates allows us to vary t...

We discuss a quasi-particle formulation of effective edge theories for the fractional quantum Hall effect. Fundamental quasi-particles for the Laughlin state with filling fraction ν = 1 3 are edge electrons of charge −e and edge quasi-holes of charge + e 3. These quasi-particles satisfy exclusion statistics in the sense of Haldane. We exploit algebraic properties of edge electrons to derive a k...

We provide numerical evidence that the ground state of a short range interaction model at ν = 1/2 is incompressible and spin-singlet for a wide range of repulsive interactions. Furthermore it is accurately described by a trial wave function studied earlier. For the Coulomb interaction we find that this wave function provides a good description of the lowest lying spin-singlet state, and propose...

A clean geometric construction is presented for the recent generalization of the Quantum Hall Effect to higher dimensional spaces. A very explicit formula is derived for the Hamiltonian in the generalized Quantum Hall Effect. This explicit formula suggests that the quantum Hall effect in even dimensions larger than two turns out to be simply copies of the two-dimensional effect.

We obtain the distribution functions for anyonic excitations classified into equivalence classes labeled by Hausdorff dimension h and as an example of such anyonic systems, we consider the collective excitations of the Fractional Quantum Hall Effect ( FQHE ). We also introduce the concept of duality between such classes, defined by h̃ = 3 − h. In this way, we confirm that the filling factors for...