Related papers: Modular Groups, Visibility Diagram and Quantum Hal…
In the fractional quantum Hall effect regime we measure diagonal ($\rho_{xx}$) and Hall ($\rho_{xy}$) magnetoresistivity tensor components of two-dimensional electron system (2DES) in gated GaAs/Al$_{x}$Ga$_{1-x}$As heterojunctions,…
Generalizing from previous work on the integer quantum Hall effect, we construct the effective action for the analog of Laughlin states for the fractional quantum Hall effect in higher dimensions. The formalism is a generalization of the…
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 perform variational Monte-Carlo calculations to show that bosons in a rotating optical lattice will form analogs of fractional quantum Hall states when the tunneling is sufficiently weak compared to the interactions and the deviation of…
We give a geometric perspective on the algebra of Drinfeld modular forms for congruence subgroups $\Gamma\leq \GL_2(\bbF_q[T]).$ In particular, we describe an isomorphism between the section ring of a line bundle on the stacky modular curve…
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…
Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed…
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…
It is shown that the Jain mapping between states of integer and fractional quantum Hall systems can be described dynamically as a perturbative renormalization of an effective Chern-Simons field theory. The effects of mirror duality…
The quantum Hall effect in ultra-high mobility GaAs/AlGaAs has been measured and plateaus are found at many different fractions. The resistivity is quantized as \rho =h/ie^2 where i exhibits many different values. The fractions 5/3, 8/5,…
Magnetic-field-induced phase transitions were studied with a two-dimensional electron AlGaAs/GaAs system. The temperature-driven flow diagram shows the features of the $\Gamma$(2) modular symmetry, which includes distorted flowlines and…
We present experimental results on the quantized Hall insulator in two dimensions. This insulator, with vanishing conductivities, is characterized by the quantization (within experimental accuracy) of the Hall resistance in units of the…
It is shown that if the carriers in the fractional quantum Hall effect are taken as geometrical excitations with quanta of charge e and magnetic flux h/2e, as proposed in a previous publication, the calculated results are compatible with…
We present a generalization of the composite Fermion picture for a muticomponent quantum Hall plasma which contains particle with different effective charges. The model predicts very well the low-lying states of a $\nu=5/2$ quantum Hall…
We consider a collection of fermions in a strong magnetic field coupled by a purely three body repulsive interaction, and predict the formation of composite fermions, leading to a remarkably rich phase diagram containing a host of…
Most of the fractions observed to date belong to the sequences $\nu=n/(2pn\pm 1)$ and $\nu=1-n/(2pn\pm 1)$, $n$ and $p$ integers, understood as the familiar {\em integral} quantum Hall effect of composite fermions. These sequences fail to…
We report on an effective vector-field theory of the fractional quantum Hall effect that takes into account projection to Landau levels. The effective theory refers to neither the composite-boson nor composite-fermion picture, but properly…
The observation of extensive fractional quantum Hall states in graphene brings out the possibility of more accurate quantitative comparisons between theory and experiment than previously possible, because of the negligibility of finite…
In this paper, we present a phenomenological picture based on the composite fermion theory, in responding to the recent discovery by Shahar et al. of a new transport regime near the transition from a $\nu=1$ quantum Hall liquid to a Hall…
I examine a model for the Hall effect in the strongly correlated regime. It emerges from an approach proposed in my previous articles [e.g. J. Phys. Chem. Solids, 65 (2004), 1507-1515; J. Geom. Phys., in press, cf. math-ph/0409023]. The…