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The formation of composite particles in the electron liquid under QHE conditions discussed by Jain in generalizing Laughlins many-particle state is considered by using a model for two-dimensional guiding center configurations. Describing…
We study experimentally the reproducible conductance fluctuations between the quantum Hall plateaus in the conductance of two-terminal submicron silicon MOSFETs. For the dramatic fluctuations at the insulator-to-first-plateau transition we…
In order to investigate whether space coordinates are intrinsically noncommutative, we make use of the Hall effect on the two-dimensional plane. We calculate the Hall conductivity in such a way that the noncommutative U(1) gauge invariance…
We study two-dimensional systems with Galilean invariance gapped under magnetic fields. When such quantum Hall systems are coupled with external sources for charge, energy, and momentum currents, they exhibit invariance under the Milne…
Recently unusual integer quantum Hall effect was observed in graphene in which the Hall conductivity is quantized as $\sigma_{xy}=(\pm 2, \pm 6, \pm 10, >...) \times \frac{e^2}{h}$, where $e$ is the electron charge and $h$ is the Planck…
The response of particle density to a dilation of a periodic potential in an insulator, with or without a fixed background potential or a magnetic field, is shown to be quantized. A similar phenomenon occurs in a quantum Hall system, where…
We study the quantum Hall effect of 2D electron gas in black phosphorus in the presence of perpendicular electric and magnetic fields. In the absence of a bias voltage, the external magnetic field leads to a quantization of the energy…
Since the experimental realisation of the integer quantised Hall effect in a two dimensional electron system subject to strong perpendicular magnetic fields in 1980, a central question has been the interrelation between the conductance…
We have performed magnetotransport experiments in the high-temperature regime (up to 50 K) of the integer quantum Hall effect for two-dimensional electron gases in semiconducting heterostructures. While the magnetic field dependence of the…
The problem of Bloch electrons in two dimensions subject to magnetic and intense electric fields is investigated, the quantum Hall conductance is calculated beyond the linear response approximation. Magnetic translations, electric evolution…
Superconducting quantum processors are a compelling platform for analog quantum simulation due to the precision control, fast operation, and site-resolved readout inherent to the hardware. Arrays of coupled superconducting qubits natively…
In the perfect conductivity problem of composite material, the electric field concentrates in a narrow region in between two inclusions and always becomes arbitrarily large when the distance between inclusions tends to zero. To characterize…
We present the adequate circular representation of charge density excitations in Quantum Hall droplets at filling factor 1. A novel set of operators describes magnetoexcitons with well defined both total and center-of-mass angular momentum.…
We find that mesoscopic conductance fluctuations in the quantum Hall regime in silicon MOSFETs display simple and striking patterns. The fluctuations fall into distinct groups which move along lines parallel to loci of integer filling…
We report an investigation of quantum Hall induced currents by simultaneous measurements of their magnetic moment and their effect on the conductance of a quantum point contact (QPC). Features in the magnetic moment and QPC resistance are…
The status of the ac quantum Hall effect is reviewed with emphasis on the theoretical development in recent years. In particular, the numerical approaches for the calculation of the frequency dependent Hall and longitudinal conductivities…
The localization behavior of noninteracting two-dimensional electrons in a random potential and strong magnetic field is of fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of power-law…
We study the quantum Hall effect in the surface states of topological insulator in the presence of a perpendicular magnetic field in the framework of edge states. Motion of Dirac fermions will form descrete Landau levels, among which a…
Measurements in magnetic fields applied at a small angle with respect to the 2D plane of the electrons of a low-density silicon MOSFET indicate that the Hall coefficient is independent of parallel field from H=0 to $H>H_{sat}$, the field…
We predict a new class of quantum Hall phenomena in completely neutral systems, demonstrating that the interplay between radial electric fields and dipole moments induces exact $e^2/h$ quantization without the need for Landau levels or…