Related papers: Four-Dimensional Quantum Hall Effect in a Two-Dime…
Symmetry, dimensionality, and interaction are crucial ingredients for phase transitions and quantum states of matter. As a prominent example, the integer quantum Hall effect (QHE) represents a topological phase generally regarded as…
The discovery of the quantum Hall effect (QHE) in 1980 marked a turning point in condensed matter physics: given appropriate experimental conditions, the Hall conductivity {\sigma}_xy of a two-dimensional (2D) electron system is exactly…
In a recent Letter we proposed a means to realize a quasicrystal with eight-fold symmetry by trapping particles in an optical potential created by four lasers. The quasicrystals obtained in this way, which are closely related to the…
In this article we review the quantum Hall physics of graphene based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed…
Commensurability is of paramount importance in numerous strongly interacting electronic systems. In the Fractional Quantum Hall effect, a rich cascade of increasingly narrow plateaux appear at larger denominator filling fractions. Rich…
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,…
This work discusses the (4+1)-dimensional generalization of the Quantum Hall Effect and its relation to axion electrodynamics.
The electronic properties of quasi two-dimensional multicomponent systems are investigated in the presence of a perpendicular magnetic field. The effects of the presence of a few valence band holes on the properties of quantum Hall systems…
Quasicrystals are nonperiodic structures having no translational symmetry but nonetheless possessing long-range order. The material properties of quasicrystals, particularly their low-temperature behavior, defy easy description. We present…
Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to novel…
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…
The quantum spin Hall effect has been observed in topological insulators using spin-orbit coupling as the probe, but it has not yet been observed in a metal. An experiment is proposed to measure the quantum spin Hall effect of an electron…
The quantum Hall effect, which exhibits a number of unusual properties, is studied in a gated 1000-nm-thick HgTe film, nominally a three-dimensional system. A weak zero plateau of Hall resistance, accompanied by a relatively small value of…
A two-dimensional array of quantum dots in a magnetic field is considered. The electrons in the quantum dots are described as unitary random matrix ensembles. The strength of the magnetic field is such that there is half a flux quantum per…
Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving…
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,…
Surface electron currents are studied for the integer quantum Hall effect in three dimensions(3D) proposed previously by Kohmoto et al. and by Koshino et al. We predict the current wraps the facets of the sample with its intensity and…
Quasicrystals are frequently encountered in condensed matter. They are important candidates for equilibrium phases from the atomic scale to the nanoscale. Here, we investigate the computational self-assembly of four quasicrystals in a…
We analysis the quantum Hall effect exhibited by a system of particles moving in a higher dimensional space. This can be done by considering particles on the Bergman ball {\bb{B}_{\rho}^d} of radius \rho in the presence of an external…
The fractional quantum Hall (FQH) effect refers to the strongly-correlated phenomena and the associated quantum phases of matter realized in a two-dimensional gas of electrons placed in a large perpendicular magnetic field. In such systems,…