Related papers: Lectures on the Quantum Hall Effect
We construct effective $\mathrm{U}(2)$ Chern-Simons-Ginzburg-Landau theories for Abelian and non-Abelian fractional quantum Hall hierarchies for those which had previously been described only through categorical data or trial wavefunctions.…
The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and…
We analyse various microscopic properties of the nematic fractional quantum Hall effect (FQHN) in the thermodynamic limit, and present necessary conditions required of the microscopic Hamiltonians for the nematic FQHE to be robust.…
Low frequency AC-measurements are commonly used to determine the voltage and currents through mesoscopic devices. We calculate the effect of the alternating Hall voltage on the recorded time-averaged voltage in the presence of a top-gate…
We generalize the fermion Chern-Simons theory for the Fractional Hall Effect (FQHE) which we developed before, to the case of bilayer systems. We study the complete dynamic response of these systems and predict the experimentally accessible…
Using the hierarchy picture of the fractional quantum Hall effect, we study the the ground state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is…
Electrons living in a two-dimensional world under a strong magnetic field - the so-called fractional quantum Hall effect (FQHE) - often manifest themselves as fractionally charged quasiparticles (anyons). Moreover, being under special…
The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the…
The double layer $\nu=2/3$ fractional quantum Hall system is studied using the edge state formalism and finite-size diagonalization subject to periodic boundary conditions. Transitions between three different ground states are observed as…
Following recent work on the quantum Hall effect on $S^4$, we solve the Landau problem on the complex projective spaces ${\bf C}P^k$ and discuss quantum Hall states for such spaces. Unlike the case of $S^4$, a finite spatial density can be…
The quantum mechanics of a system of charged particles interacting with a magnetic field on Riemann surfaces is studied. We explicitly construct the wave functions of ground states in the case of a metric proportional to the Chern form of…
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…
Stacked two dimensional electron systems in transverse magnetic fields exhibit three dimensional fractional quantum Hall phases. We analyze the simplest such phases and find novel bulk properties, e.g., irrational braiding. These phases…
Motivated by recent transport experiments, we theoretically study the quantum Hall effect in topological semimetal films. Owing to the confinement effect, the bulk subbands originating from the chiral Landau levels establish energy gaps…
We review the construction of a low-energy effective field theory and its state space for "abelian" quantum Hall fluids. The scaling limit of the incompressible fluid is described by a Chern-Simons theory in 2+1 dimensions on a manifold…
We consider the influence of an external periodic potential on the fractional quantum Hall effect of two-dimensional interacting electron systems. For many electrons on a torus, we find that the splitting of incompressible ground state…
This paper is a lab tutorial (and a theory primer) for the integral quantum Hall effect experiment as conducted at Applied Solid State Physics, University of Bochum, Germany.
We report on an effective gauge theory of double-layer quantum Hall systems, that is constructed via bosonization from the response of incompressible states without referring to composite bosons and fermions. It is pointed out that…
The quantum Hall effect is generally understood for free electron gases, in which topologically protected edge states between Landau levels (LLs) form conducting channels at the edge of the sample. In periodic crystals, the LLs are…
By carefully considering a family of wave functions for Skyrmions in simple quantum Hall states, whose members are labelled by a non-negative integer and which properly generalizes the traditional Laughlin quasiparticle, we argue that the…