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We study the relation between quantum entanglement and electron correlation in quantum chemistry calculations. We prove that the Hartree-Fock (HF) wave function does not violate Bell's inequality, thus is not entangled while the…
In this work we investigate the electrostatic properties of two dimensional electron system (2DES) in the integer quantum Hall regime. The alternating screening properties of compressible and incompressible strips are formed due to edge…
We derive the implications of particle-vortex duality for the electromagnetic response of Quantum Hall systems beyond the linear-response regime. This provides a first theoretical explanation of the remarkable duality which has been…
A theory is developed for the paired even-denominator fractional quantum Hall states in the lowest Landau level. We show that electrons bind to quantized vortices to form composite fermions, interacting through an exact instantaneous…
We numerically study a 5/2 fractional quantum Hall system with even number of electrons using the exact diagonalization where both the strong Landau level (LL) mixing and a finite width of the quantum well have been considered and adapted…
We investigate the quantum Hall effect in a single Landau level in the presence of a square superlattice of $\delta$-function potentials. The interplay between the superlattice spacing $a_s$ and the magnetic length $\ell_B$ in clean system…
We use the Kubo formalism to calculate the transresistivity $\rho_{21}$ for carriers in coupled quantum wells in a large perpendicular magnetic field $B$. We find that $\rho_{21}$ is enhanced by approximately 50--100 times over that of the…
A theory of transport in the quantum Hall regime is developed for separately contacted double-layer electron systems. Inter-layer tunneling provides a channel for equilibration of the distribution functions in the two layers and influences…
We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that irrespective of the interaction strength the Hall conductivity is given by the filling fraction of Landau levels averaged over…
Dynamical Hall conductivity {\sigma}_H({\omega}) of a 2D electron gas with impurities in the perpendicular magnetic field is analyzed. Plateau-like behavior at low frequencies as well as at high frequencies provided the complete filling of…
The tunneling conductance between two parallel 2D electron systems has been measured in a regime of strong interlayer Coulomb correlations. At total Landau level filling $\nu_T=1$ the tunnel spectrum changes qualitatively when the boundary…
We review the theoretical basis and understanding of electronic interactions in graphene Landau levels, in the limit of strong correlations. This limit occurs when inter-Landau-level excitations may be omitted because they belong to a…
Coulomb drag resulting from interlayer electron-electron scattering in double layer 2D electron systems at high magnetic field has been measured. Within the lowest Landau level the observed drag resistance exceeds its zero magnetic value by…
We numerically investigate the effect of electron correlation on the integer quantum Hall effect in a square lattice. Increasing the correlation strength via the effective onsite repulsion parameter $U$ degrades the quantization of $\nu =…
We present a simple classification of the different liquid and solid phases of quantum Hall systems in the limit where the Coulomb interaction between the electrons is significant, i.e. away from integral filling factors. This…
Double-layer electron systems in the quantum Hall regime have excitonic condensate ground states when the layers are close together and the total Landau level filling factor is close to an odd integer. In this paper we discuss the…
We study the Hall constant in a homogeneous two-dimensional fluid of correlated electrons immersed in a perpendicular magnetic field, with special focus on the regime of low carrier density. The model consists of a one-band tight-binding…
I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic…
We study the effect of interlayer Coulomb interaction in an electronic double layer. Assuming that each of the layers consists of a bipartite lattice, a sufficiently strong interlayer interaction leads to an interlayer pairing of electrons…
Weakly disordered bilayer quantum Hall systems at filling factor $\nu=1$ show spontaneous interlayer phase coherence if the layers are sufficiently close together. We study the collective modes in the system, the current-voltage…