Related papers: An algebraic approach to FQHE variational wave fun…
We establish the quantum mechanics of composite fermions based on the dipole picture initially proposed by Read. It comprises three complimentary components: a wave equation for determining the wave functions of a composite fermion in ideal…
An important development in the field of the fractional quantum Hall effect has been the proposal that the 5/2 state observed in the Landau level with orbital index $n = 1$ of two dimensional electrons in a GaAs quantum well originates from…
We achieve an explicit construction of the lowest Landau level (LLL) projected wave functions for composite fermions in the periodic (torus) geometry. To this end, we first demonstrate how the vortex attachment of the composite fermion (CF)…
Originally proposed by Read [1] and Jain [2], the so-called "composite-fermion" is a phenomenological attachment of two infinitely thin local flux quanta seen as nonlocal vortices to two-dimensional (2D) electrons embedded in a strong…
In this paper we prove that any multi-resolution analysis of $\Lc^2(\R)$ produces, for some values of the filling factor, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translated, gives…
The structure of fractional fillings of higher Landau levels including spin subbands is systematically derived for the first time. Using topology-type commensurability arguments for 2D charged system in the presence of strong quantizing…
We use exact numerical diagonalization in the search of fractional quantum Hall states with non-Abelian quasiparticle statistics. For the (most promising) states in a partially filled second Landau level, the search is narrowed to the range…
The fractional quantum Hall (FQH) effect arises from strong electron correlations in a quantising magnetic field, and features exotic emergent phenomena such as electron fractionalisation. Using the diagrammatic Monte Carlo approach with…
Quantum gases are used to simulate the physics of the lowest Landau level (LLL) with neutral atoms, which in the simplest setup is achieved by rotating the gas at the confining harmonic trap frequency, a requirement that is difficult to…
The fractional quantum anomalous Hall effect (FQAHE), the analog of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking. The…
The single-particle spectral function for an incompressible fractional quantum Hall state in the presence of a scalar short-ranged attractive impurity potential is calculated via exact diagonalization within the spherical geometry. In…
While the integer quantum Hall effect of composite fermions manifests as the prominent fractional quantum Hall effect (FQHE) of electrons, the FQHE of composite fermions produces further, more delicate states, arising from a weak residual…
Due to its fourfold spin-valley degeneracy, graphene in a strong magnetic field may be viewed as a four-component quantum Hall system. We investigate the consequences of this particular structure on a possible, yet unobserved, fractional…
A novel model of complex quantum harmonic oscillator is found to account for the observed Fractional quantum Hall effect (FQHE). The sequences of the observed FQHE conductivity and charge are explained. The two sequences are found to…
We present a set of explicit trial wavefunctions for the filling factors \nu=n/(2n\pm 1) and \nu=1/2 in the symmetric gauge. We show that the zeroes of the wavefunction, except those dictated by the Fermi statistics, are detached from the…
We present a theoretical framework to describe the integer quantum Hall effect (IQHE) in three-dimensional (3D) electron systems. This extends our previous single-electron approach, which was successfully applied to two-dimensional (2D)…
We comprehensively show the topological structure--order of zeros felt by an electron at the positions of other electrons --for the enigmatic filling factor 5/2 at the "Pfaffian-shift" in a spherical geometry. A set of linearly independent…
We study fractional boundary charges (FBCs) for two classes of strongly interacting systems. First, we study strongly interacting nanowires subjected to a periodic potential with a period that is a rational fraction of the Fermi wavelength.…
We report an experimental investigation of fractional quantum Hall effect (FQHE) at the even-denominator Landau level filling factor $\nu$ = 1/2 in very high quality wide GaAs quantum wells, and at very high magnetic fields up to 45 T. The…
We consider 2D fermions on a plane with a perpendicular magnetic field, described by Landau levels. It is wellknown that, semiclassically, restriction to the lowest Landau levels (LLL) implies two constraints on a 4D phase space, that…