Related papers: Incompressibility Estimates for the Laughlin Phase
We investigate fractional quantum Hall states for model interactions restricted to a repulsive hard-core. When the hard-core excludes relative angular momentum $m=1$ between spinless electrons the ground state at Landau level filling factor…
In a previous paper we have proven that any multi-resolution analysis of $L^2(\R)$ produces, for even values of the inverse filling factor and for a square lattice, a single-electron wave function of the lowest Landau level (LLL) which,…
The energy spectra and wavefunctions of up to 14 interacting quasielectrons (QE's) in the Laughlin nu=1/3 fractional quantum Hall (FQH) state are investigated using exact numerical diagonalization. It is shown that at sufficiently high…
The entanglement entropy of the incompressible states of a realistic quantum Hall system are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is believed to carry…
In the absence of disorder, the degeneracy of a Landau level (LL) is $N=BA/\phi_0$, where $B$ is the magnetic field, $A$ is the area of the sample and $\phi_0=h/e$ is the magnetic flux quantum. With disorder, localized states appear at the…
We study two-dimensional (2D) droplets of noninteracting electrons in a strong magnetic field, placed in a confining potential with arbitrary shape. Using semiclassical methods adapted to the lowest Landau level, we obtain near-Gaussian…
Motivated by the quasiparticle wavefunction in the composite fermion (CF) theory for fractional quantum Hall filling factor $\nu = 1/m$, I consider a suitable quasiparticle operator in differential form, as a modified form of Laughlin's…
The fractional quantum Hall effect (FQHE), observed in two-dimensional (2D) charged particles at high magnetic fields, is one of the most fascinating, macroscopic manifestations of a many-body state stabilized by the strong Coulomb…
The wavefunction method provides us with a useful tool to describe electron correlations in solids at the ground state. In this paper we review the recent development of the momentum-dependent local ansatz wavefunction (MLA). It is…
The intriguing re-entrant integer quantized Hall states recently discovered in high Landau levels of high-mobility 2D electron systems are found to exhibit extremely non-linear transport. At small currents these states reflect insulating…
The compressibility of a two-dimensional electron system with spin in a spatially correlated random potential and a quantizing magnetic field is investigated. Electron-electron interaction is treated with the Hartree-Fock method. Numerical…
A model system is considered where two dimensional electrons are confined by a harmonic potential in one direction, and are free in the other direction. Ground state in strong magnetic fields is investigated through numerical…
We review the basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field. One of its most salient features is the relativistic quantum Hall effect the observation of which has been the…
Nowadays a vast literature is available on the Hele-Shaw or incompressible limit for nonlinear degenerate diffusion equations. This problem has attracted a lot of attention due to its applications to tissue growth and crowd motion modelling…
Graphene and its multilayers have attracted considerable interest owing to the fourfold spin and valley degeneracy of their charge carriers, which enables the formation of a rich variety of broken-symmetry states and raises the prospect of…
We propose a new way for describing the transition between two quantum Hall effect states with different filling factors within the framework of rational conformal field theory. Using a particular class of non-unitary theories, we…
The Schrodinger equation for an interacting spinless electron gas in a nonuniform magnetic field admits an exact solution in Jastrow product form when the fluctuations in the magnetic field track the fluctuations in the scalar potential.…
A subtle relation between Quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest…
We consider a system of a incompressible quantum Hall liquid in close proximity to a parabolic quantum dot containing a few electrons. We observe a significant influence of the interacting electrons in the dot on the excitation spectrum of…
By developing an algorithm for evaluating the basis states for the composite fermions with negative effective magnetic field, we perform the composite-fermion-diagonalization study for the fully spin-polarized fractional quantum Hall states…