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The intrinsic geometric degree of freedom that was proposed to determine the optimal correlation energy of the fractional quantum Hall states, is analyzed for quantum confined planar electron systems. One major advantage in this case is…
We present an effective theory for the bulk Fractional Quantum Hall states in spin-polarized bilayer and spin-1/2 single layer two-dimensional electron gases (2DEG) in high magnetic fields consistent with the requirement of global gauge…
The present theory has investigated the FQHE without any quasi-particle. The electric field due to the Hall voltage is taken into consideration. We find the ground state where the electron configuration is uniquely determined so as to have…
The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems is explained by the emergent composite fermions (CF) out of ordinary electrons. It is possible to write down explicit wavefunctions explaining many if…
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 review recent investigations of the femtosecond non-linear optical response of the two-dimensional electron gas (2DEG) in a strong magnetic field. We probe the Quantum Hall (QH) regime for filling factors $\nu \sim 1$. Our focus is on…
Low-energy transport in quantum Hall states is carried through edge modes, and is dictated by bulk topological invariants and possibly microscopic Boltzmann kinetics at the edge. Here we show how the presence or breaking of symmetries of…
Quantum Hall edge channels can be combined with metallic regions to fractionalize electrons and form correlated impurity models. We study a minimal device, that has been experimentally achieved quite recently, with two floating islands…
The energy gaps appearing in the fractional quantum Hall effect (FQHE) remain an essential aspect of the investigation. Moreover, the plateau widths in the Hall resistance have been considered simply an effect of disorder as in the integral…
We investigate the ground-state structure of the bilayer quantum Hall system at the filling factor $\nu =2$. Making an exact analysis of the ground state in the SU(4)-invariant limit, we include all other interactions as small perturbation.…
Two laterally adjacent quantum Hall systems separated by an extended barrier of a thickness on the order of the magnetic length possess a complex Landau band structure in the vicinity of the line junction. The energy dispersion is obtained…
The fractional quantum Hall effect (FQHE) stands as a quintessential manifestation of an interacting two-dimensional electron system. One of FQHE's most fundamental characteristics is the energy gap separating the incompressible ground…
We look for manifestations of quantum interference effects in the Seebeck coefficient of a molecular junction, when the electronic conductance exhibits pronounced destructive interference features due to the presence of quasi-degenerate…
Recently, generalizations of quantum Hall effects (QHE) have been made from 2D to 4D and 8D by considering their mathematical frameworks within complex (C), quaternion (H) and octonion (O) compact (gauge) Lie algebra domains. Just as QHE in…
Double barrier heterostructures are model systems for the study of electron tunneling and discrete energy levels in a quantum well (QW). Until now resonant tunneling phenomena in metallicQW have been observed for limited thicknesses (1-2…
We propose a device, consisting of a Hall bar with two weak barriers, that can be used to study quantum interference effects in a strongly correlated system. We show how the device provides a way of measuring the fractional charge and…
We study two dimensional electron systems confined in wide quantum wells whose subband separation is comparable with the Zeeman energy. Two N = 0 Landau levels from different subbands and with opposite spins are pinned in energy when they…
We investigate the effect on a Quantum Hall (QH) liquid of its coupling to 3+1 dimensional dynamical electromagnetism, which renders the system gapless. We calculate both the Hall and longitudinal resistances, $\rho_H$ and $\rho_L$, in the…
Owing to their wide tunability, spin- and valley internal degrees of freedom, and low disorder, graphene heterostructures are emerging as a promising experimental platform for fractional quantum Hall (FQH) studies. Surprisingly, however,…
The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded and brought into focus the concept of topological order in physics. The topologically protected quantum Hall edge states are of crucial importance to the QH…