Related papers: A systematic study of non-ideal contacts in intege…
The von Neumann lattice representation is a convenient representation for studying several intriguing physics of quantum Hall systems. In this formalism, electrons are mapped to lattice fermions. A topological invariant expression of the…
The symmetry properties of the resistance of mesoscopic samples in the quantum Hall regime are investigated. In addition to the reciprocity relation, our samples obey new symmetries, that relate resistances measured with different contact…
We have conducted an experimental study of the linear transport properties of the magnetic-field induced insulating phase which terminates the quantum Hall (QH) series in two dimensional electron systems. We found that a direct and simple…
The transversal and longitudinal resistance in the quantum Hall effect regime was measured in a Si MOSFET sample in which a slot-gate allows one to vary the electron density and filling factor in different parts of the sample. In case of…
We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the $\nu=2$ and the $\nu=1$ quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall…
We investigate a gapped two-dimensional nodal-line semimetal subjected to a perpendicular magnetic field. We identify an unusual pattern for Landau levels, where the energy of Landau levels first decreases and then starts increasing versus…
The edge states in the integer quantum Hall effect are known to be significantly affected by electrostatic interactions leading to the formation of compressible and incompressible strips at the boundaries of Hall bars. We show here, in a…
Using a mapping of a layered three-dimensional system with significant inter-layer tunneling onto a spin-Hamiltonian, the phase diagram in the strong magnetic field limit is obtained in the semi-classical approximation. This phase diagram,…
We investigate the phenomenon of integer quantum Hall effect in a square lattice, subjected to a perpendicular magnetic field, through Landauer-B\"uttiker formalism within the tight-binding framework. The oscillating nature of longitudinal…
The fate of integer quantum Hall effect (IQHE) at weak magnetic field is studied numerically in the presence of {\it correlated} disorders. We find a systematic {\it float-up} and {\it merging} picture for extended levels on the low-energy…
The observed quantization of the Hall conductivity in graphene at high magnetic fields is explained as being due to the dynamically generated spatial modulation of either the electron spin or the density, as decided by the details of…
By studying the quantum Hall effect of stationary states with high values of injected current using a von Neumann lattice representation, we found that broadening of extended state bands due to a Hall electric field occurs and causes the…
Integer and fractional quantum Hall effects were studied with different physics models and explained by different physical mechanisms. In this paper, the common physical mechanism for integer and fractional quantum Hall effects is studied,…
The quantum Hall effect is studied numerically in modulated two-dimensional electron systems in the presence of disorder. Based on the scaling property of the Hall conductivity as well as the localization length, the critical energies where…
We study the quantum Hall effect inside a gravitational field. First, we review the influence of the gravitational field of the Earth on the quantum Hall effect. Taking the gravitational field of the Earth to be uniform along the vertical…
We present the theoretical description for a class of experimental setups that measure quantum Hall coefficients in ferromagnet-topological insulator-ferromagnet (FM-TI-FM) junctions. We predict that varying the magnetization direction in…
In this Chapter, we give a brief review of the state of the art of theoretical and experimental studies of synthetic magnetic fields and quantum Hall effects in ultracold atomic gases. We focus on integer, spin, and fractional Hall effects,…
The phase diagram of integer quantum Hall effect is numerically determined in the tight-binding model, which can account for overall features of recently obtained experimental phase diagram. In particular, the quantum Hall plateaus are…
In the context of experimental advances in the realization of artificial magnetic fields in quantum gases, we discuss feasible schemes to extend measurements of the Hall polarization to a study of the Hall voltage, allowing for direct…
We report on theoretical and experimental investigations of the integer quantized Hall effect in narrow channels at various mobilities. The Hall bars are defined electrostatically in two-dimensional electron systems by biasing metal gates…