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It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. Fractional statistics can be extended to nonabelian statistics and examples can be constructed…
The scaling behavior near the transition between plateaus of the Integer Quantum Hall Effect (IQHE) has traditionally been interpreted on the basis of a two-parameter renormalization group (RG) flow conjectured from Pruisken's non-linear…
We examine the effects of electron-electron interactions on transport between edge states in a multilayer integer quantum Hall system. The edge states of such a system, coupled by interlayer tunneling, form a two-dimensional, chiral metal…
Quantum transport properties in quantum Hall wires in the presence of spatially correlated disordered magnetic fields are investigated numerically. It is found that the correlation drastically changes the transport properties associated…
The quantum Hall effect in graphene p-n junctions is studied numerically with emphasis on the effect of disorder at the interface of two adjacent regions. Conductance plateaus are found to be attached to the intensity of the disorder, and…
Due to the lack of simulation tools that take into account the actual geometry of complicated quantum Hall samples there are lots of experiments that are not yet fully understood. Already some years ago R. G. Mani recorded a shift of the…
We present a new theoretical approach for the integer quantum Hall effect, which is able to describe the inter-plateau transitions as well as the transition to the Hall insulator. We find two regimes (metallic and insulator like) of the top…
Using the Calogero model as an example, we show that the transport in interacting non-dissipative electronic systems is essentially non-linear. Non-linear effects are due to the curvature of the electronic spectrum near the Fermi energy. As…
In order to fully characterize the noise associated with electron transport, with its severe consequences for solid-state quantum information systems, the theory of full counting statistics has been developed. It accounts for correlation…
We study the influence of short-range electron-electron interactions on scaling behavior near the integer quantum Hall plateau transitions. Short-range interactions are known to be irrelevant at the renormalization group fixed point which…
These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The…
A two-dimensional harmonic oscillator, when rotated by the oscillator frequency, generates Landau-like levels. A further cranking results in condensates and gaps resembling the fractional quantum Hall effect. For a filling fraction…
Short-range electron-electron interactions are incorporated into the network model of the integer quantum Hall effect. In the presence of interactions, the electrons, propagating along one link, experience exchange scattering off the…
Using simultaneous measurements of the attenuation and velocity of surface acoustic waves propagating along GaAs/Al$_{0.3}$Ga$_{0.7}$As heterostructures, complex ac conductance of the latters has been determined. In the magnetic fields…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations…
In the Hall effect, a voltage drop develops perpendicularly to the current flow in the presence of a magnetic field, leading to a transverse Hall resistance. Recent developments with quantum simulators have unveiled strongly correlated and…
We investigate the behavior of the quantized Hall conductivity in a two-dimensional quantum system under rotating effects, a uniform magnetic field, and an Aharonov-Bohm (AB) flux tube. By varying the angular velocity and the AB flux, we…
We study both the continuous model and the discrete model of the integer quantum Hall effect on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper [CHMM]. Here we model impurities, that is we…
Using the path-integral formalism, we show that photons possess a nontrivial quantum metric in momentum space. We derive the semiclassical action and equations of motion by taking into account the quantum metric. In media with a spatially…