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We present a microscopic theory of the Hall current in the bilayer quantum Hall system on the basis of noncommutative geometry. By analyzing the Heisenberg equation of motion and the continuity equation of charge, we demonstrate the…

I discuss in an elementary and self-contained way the nature of the current-carrying state in Hall superfluids. The explicit connection of fractional charge and rationality of the filling fraction $\nu$ with quantization of angular…

We systematically study the acousto-current of two-dimensional electron systems in the integer and fractional quantum Hall regimes using surface acoustic waves. We are able to separate the co-existing acoustic scattering and drag, when…

Observations of electron-hole asymmetry in transport through graphene devices at high magnetic field challenge prevalent models of the graphene quantum Hall effect. Here, we study this asymmetry both in conventional magnetotransport and in…

The edge structure of the $\nu=2/3$ fractional quantum Hall state has been studied for several decades but recent experiments, exhibiting upstream neutral mode(s), a plateau at a Hall conductance of $\frac{1}{3}( e^2/h)$ through a quantum…

We derive electromagnetomotive force fields for charged particles moving in a rotating Hall sample, satisfying a twofold U(1) gauge invariance principle. It is then argued that the phase coherence property of quantization of the line…

The longitudinal and Hall resistances have recently been measured for quantum Hall bilayers at total filling $\nu=1$ in the superfluid state with interlayer pairing, both for currents flowing parallel to one another and for "counterflowing"…

Recent experimental work on locally gated graphene layers resulting in p-n junctions have revealed quantum Hall effect in their transport behavior. We explain the observed conductance quantization which is fractional in the bipolar regime…

The Moore-Read Pfaffian $\nu=5/2$ quantum Hall state is a p-wave super-conductor of composite fermions. Small deviations from $\nu=5/2$ result in the formation of an array of vortices within this super-conductor, each supporting a Majorana…

A theoretical calculation is presented of current noise which is due charge fractionalization, in two interacting edge channels in the integer quantum Hall state at filling factor $\nu=2$. Because of the capacitive coupling between the…

We revisit the physics of hole-conjugate Fractional Quantum Hall (FQH) phases characterized by counter-propagating edge channels at filling factors above 1/2. We propose a minimal and intuitive model that successfully accounts for all…

A quasiclassical theory for dc magnetotransport in a modulated quantum Hall system near filling factor $\nu={1/2}$ is presented. A weak one-dimensional electrostatic potential acts on the two-dimensional electron gas. Closed form analytic…

Motivated by surprises in recent experimental findings, we study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a…

The nature of edge state transport in quantum Hall systems has been studied intensely ever since Halperin [1] noted its importance for the quantization of the Hall conductance. Since then, there have been many developments in the study of…

We report on the properties of a system of interacting electrons in a narrow channel in the quantum Hall effect regime. It is shown that an increase in the strength of the Coulomb interaction causes abrupt changes in the width of the…

It is commonly believed that the current response of an electron fluid to a mechanical force (such as an electric field) or to a ``statistical force" (e.g., a gradient of chemical potential) are governed by a single linear transport…

We extend the quantum Hall matrix model to include couplings to external electric and magnetic fields. The associated current suffers from matrix ordering ambiguities even at the classical level. We calculate the linear response at low…

This paper describes an experimental identification and characterization of a new low temperature transport regime near the quantum Hall-to-insulator transition. In this regime, a wide range of transport data are compactly described by a…

Motivated by the recent experiment by Grayson et.al., we investigate a non-ohmic current-voltage characteristics for the tunneling into fractional quantum Hall liquids. We give a possible explanation for the experiment in terms of the…

This paper comprises a review of our recent works on fractional chiral modes that emerge due to edge reconstruction in integer and fractional quantum Hall (QH) phases. The new part added is an analysis of edge reconstruction of the $\nu =…