Related papers: Integer Quantum Hall Effect for Lattice Fermions
The quasi-quantized Hall effect (QQHE) is the three-dimensional (3D) counterpart of the integer quantum Hall effect (QHE),exhibited only by two-dimensional (2D) electron systems. It has recently been observed in layered materials,…
Non-interacting topological states of matter can be realized in band insulators with intrinsic spin-orbital couplings as a result of the nontrivial band topology. In recent years, the possibility of realizing novel interaction-driven…
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 behavior of the extended states of a two-dimensional electron system in silicon in a magnetic field, B. Our results show that the extended states, corresponding to the centers of different Landau levels, merge with the lowest…
Statistics of level spacing and magnetization are studied for the phase diagram of the integer quantum Hall effect in a 2D finite lattice model with Anderson disorder.
The unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at $\nu=2+6/13$~ [Kumar \emph{et al.}, Phys. Rev. Lett. {\bf 105}, 246808 (2010)] offers a clue into the physical mechanism of the FQHE in the second Landau level…
The quantum anomalous Hall effect (QAHE) is a quantum phenomenon in which a two-dimensional system exhibits a quantized Hall resistance $h/e^2$ in the absence of magnetic field, where $h$ is the Planck constant and $e$ is the electron…
We present a supersymmetric description of the quantum Hall effect (QHE) in graphene. The noninteracting system is supersymmetric separately at the so-called K and K' points of the Brillouin zone corners. Its essential consequence is that…
We report low temperature electronic transport results on the fractional quantum Hall effect of composite fermions at Landau level filling nu = 4/11 in a very high mobility and low density sample. Measurements were carried out at…
We numerically study the interplay of band structure, topological invariant and disorder effect in two-dimensional electron system of graphene in a magnetic field. Two \emph{distinct} quantum Hall effect (QHE) regimes exist in the energy…
Collective modes of exotic quantum fluids reveal underlying physical mechanisms responsible for emergent complex quantum ground states. We observe unexpected new collective modes in the fractional quantum Hall (FQH) regime:…
We study an unconventional quantum Hall effect for the surface states of ultrathin Floquet topological insulators in a perpendicular magnetic field. The resulting band structure is modified by photon dressing and the topological property is…
We study disorder induced transition between quantum Hall states and insulator state in a {\it lattice} model. We find the positions of the extended states do not change as disorder strength is varied. As a consequence, there are direct…
We show that, when graphene is subjected to an appropriate one-dimensional external periodic potential, additional branches of massless fermions are generated with nearly the same electron-hole crossing energy as that at the original Dirac…
When phonons couple to fermions in 2D semimetals, the interaction may turn the system into an insulator. There are several insulating phases in which the time reversal and the sublattice symmetries are spontaneously broken. Examples are…
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…
In a GaAs/AlGaAs quantum well of electron density 1x10^{11} cm^{-2} we observe a fractional quantum Hall effect (FQHE) at filling factors nu=4/11, and 5/13, and weaker states at nu=6/17, 4/13, 5/17 and 7/11. These sequences of fractions do…
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 quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and…
We give an overview of the Integer Quantum Hall Effect. We propose a mathematical framework using Non-Commutative Geometry as defined by A. Connes. Within this framework, it is proved that the Hall conductivity is quantized and that…