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We investigate the quantum Hall problem in the lowest Landau level in two dimensions, in the presence of an arbitrary number of $\delta$-function potentials arranged in different geometric configurations. When the number of delta functions…
Among the various geometries to study the fractional quantum Hall effect in two dimensional electron gas, the Corbino disc owns the advantage to probe the bulk properties directly. In this work we explore the influence of in-plane electric…
In this report, we study ultra-high-mobility two-dimensional (2D) electron/hole systems with high precision capacitance measurement. We find that the capacitance charge appears only at the fringe of the gate at high magnetic field when the…
Electrons that are confined to a single Landau level in a two dimensional electron gas realize the effects of strong electron-electron repulsion in its purest form. The kinetic energy of individual electrons is completely quenched and all…
We show that, at low temperatures, macroscopic inhomogeneities of the electron density in the interior of a finite sample cause a reduction in the measured conductivity peak heights $\sigma_{xx}^{\rm max}$ compared to the universal values…
The temperature dependence of an integer Quantum Hall effect transition is studied in a sample where the disorder is dominated by short-ranged potential scattering. At low temperatures the results are consistent with a $(T/T_0)^{\kappa}$…
Quantum-mechanical fluctuations between competing phases at $T=0$ induce exotic finite-temperature collective excitations that are not described by the standard Landau Fermi liquid framework. These excitations exhibit anomalous temperature…
Topological states of matter are characterized by topological invariant, which are physical quantities whose values are quantized and do not depend on details of the measured system. Of these, the easiest to probe in experiments is the…
We investigate fractional quantum Hall effect at finite temperature using a fermion Chern-Simons field theoretical approach. In the absence of impurity scattering, the essential aspects of fractional quantum Hall effect, such as the…
The in-plane Hall coefficient $R_{H}(T)$ of CeRhIn$_{5}$, CeIrIn$_{5}$, and CeCoIn$_{5}$ and their respective non-magnetic lanthanum analogs are reported in fields to 90 kOe and at temperatures from 2 K to 325 K. $R_{H}(T)$ is negative,…
The edge and bulk structure of Landau levels (LLs) in a wide channel at the $ \nu =1$ quantum Hall regime is calculated for not-too-low temperatures, $\hbar \omega_{c} \gg k_{B}T\gg \hbar v_{g}/2\ell_{0}$, where $v_{g}$ is the group…
We derive exact physical consequences of particle-hole symmetry of the $\nu=1/2$ state of electrons in a strong magnetic field. We show that if the symmetry is not spontaneously broken, the Hall conductivity and the susceptibility satisfy…
We show that a suitable combination of geometric frustration, ferromagnetism and spin-orbit interactions can give rise to nearly flat bands with a large bandgap and non-zero Chern number. Partial filling of the flat band can give rise to…
We present Hall effect measurements on highly oriented pyrolytic graphite that indicate the occurrence of the integer quantum-Hall-effect. The evidence is given by the observation of regular plateau-like structures in the field dependence…
We report experimental studies of disorder-induced transitions between quantum-Hall, metallic, and insulating states in a very dilute two-dimensional electron system in silicon at a magnetic field corresponding to Landau level filling…
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…
The design, manufacture and characterisation of an inexpensive, temperature controlled vacuum chamber with millikelvin stability for electrical transport measurements at and near room temperature is reported. A commercially available…
We propose a scenario to understand the puzzling features of the recent experiment by Kang and coworkers on tunneling between laterally coupled quantum Hall liquids by modeling the system as a pair of coupled chiral Luttinger liquid with a…
A quantum critical point (QCP) develops in a material at absolute zero when a new form of order smoothly emerges in its ground state. QCPs are of great current interest because of their singular ability to influence the finite temperature…
The conductance of a two-dimensional electron gas at the transition from one quantum Hall plateau to the next has sample-specific fluctuations as a function of magnetic field and Fermi energy. Here we identify a universal feature of these…