Related papers: A new approach to the ground state of quantum-Hall…
In a recent paper (arXiv:2206.05152v4), using the exact diagonalization technique, I calculated the energy and other physical properties (electron density, pair correlation function) of a system of $N\le 7$ two-dimensional electrons at the…
I present a new approach to the many-body ground state of quantum-Hall systems. The method describes the behavior of a two-dimensional electron system at all Landau-level filling factors $\nu$, continuously as a function of magnetic field,…
The fractional quantum Hall effect was experimentally discovered in 1982. It was observed that the Hall conductivity $\sigma_{yx}$ of a two-dimensional electron system is quantized, $\sigma_{yx}=e^2/3h$, in the vicinity of the Landau level…
New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They…
The fractional quantum Hall effect in 2D electron gases submitted to large magnetic fields remains one of the most striking phenomena in condensed matter physics. Historically, the first observed signature is a Hall resistance quantized to…
The competition between liquid and solid states of strongly correlated electron systems occurs in a novel way in a strong magnetic field. The fact that certain Landau level filling factors are especially favorable for the formation of…
In the strong magnetic field fractional quantum Hall regime, electrons in a two-dimensional electron system are confined to their lowest Landau level. Because of the macroscopic Landau level degeneracy nearly all physical properties at low…
At filling factor $\nu=1/m$, $m$ odd integer, I present variational ground-state and excited-state wave functions, of two-dimensional electron system with homogeneous ion background, that show the condensation into a liquid-crystal state.…
We demonstrate that the two-dimensonal electron system in a strong perpendicular magnetic field has stable states which break rotational but not translational symmetry. The Laughlin fluid becomes unstable to these states in quantum wells…
On the basis of our previous studies on energy levels and wave functions of single electrons in a strong magnetic field, the energy levels and wave functions of non-interacting electron gas system, electron gas Hall surface density and Hall…
We report a theoretical analysis of the half-polarized quantum Hall states observed in a recent experiment. Our numerical results indicate that the ground state energy of the quantum Hall $\nu= 2/3$ and $\nu= 2/5$ states versus spin…
We construct a generalized Laughlin-liquid wave function and a variational electron solid wave function when the magnetic field is tilted. The energy of the liquid state is evaluated by Monte Carlo methods while the energy of the solid…
In the framework of a recently developed model of interacting composite fermions, we calculate the energy of different solid and Laughlin-type liquid phases of spin-polarized composite fermions. The liquid phases have a lower energy than…
States of strongly interacting particles are of fundamental interest in physics, and can produce exotic emergent phenomena and topological structures. We consider here two-dimensional electrons in a magnetic field, and, departing from the…
To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many…
We have observed in a low density two-dimensional hole system (2DHS) of extremely high quality (with hole density p=1.6x10^{10} cm^{-2} and mobility \mu=0.8x10^6 cm^2/Vs) that, as the 2DHS is continuously tilted with respect to the…
We study electronic structures of quasi-two-dimensional finite electron systems in high magnetic fields. The solutions in the fractional quantum Hall regime are interpreted as quantum liquids of electrons and off-electron vortices. The…
We present a numerical study of fractional quantum Hall liquid at Landau level filling factor $\nu=2/3$ in a microscopic model including long-range Coulomb interaction and edge confining potential, based on the disc geometry. We find the…
We have calculated the exchange-energy contribution to the total energy of quasi-two-dimensional hole systems realized by a hard-wall quantum-well confinement of valence-band states in typical semiconductors. The magnitude of the exchange…
We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr\"odinger perturbation theory, using the Sturmian…