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Two-dimensional electron gases in strong magnetic fields provide a canonical platform for realizing a variety of electronic ordering phenomena. Here we review the physics of one intriguing class of interaction-driven quantum Hall states:…
We calculate numerically the spectrum of disordered electrons in the lowest Landau level at filling factor 1/5 using the self-consistent Hartree-Fock approximation for systems containing up to 400 flux quanta. Special attention is paid to…
Transport measurements at cryogenic temperatures through a few electron top gated quantum dot fabricated in a silicon/silicon-germanium heterostructure are reported. Variations in gate voltage induce a transition from an isolated dot toward…
We examine the relation between different electronic transport phenomena in a Fabry-Perot interferometer in the fractional quantum Hall regime. In particular, we study the way these phenomena reflect the statistics of quantum Hall…
A set of localized, non-Abelian anyons - such as vortices in a p_x + i p_y superconductor or quasiholes in certain quantum Hall states - gives rise to a macroscopic degeneracy. Such a degeneracy is split in the presence of interactions…
Materials hosting topologically protected non-Abelian zero modes offer the exciting possibility of storing and manipulating quantum information in a manner that is protected from decoherence at the hardware level. In this work, we study the…
We study resonant tunneling through quantum-dot systems in the presence of strong Coulomb repulsion and coupling to the metallic leads. Motivated by recent experiments we concentrate on (i) a single dot with two energy levels and (ii) a…
Multiple topologically distinct quantum Hall phases can occur at the same Landau level filling factor. It is a major challenge to distinguish between these phases as they only differ by the neutral modes, which do not affect the charge…
The edges of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime are divided into alternating metallic and insulating strips, with their widths determined by the energy gaps of the QHE states and the electrostatic…
We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state which is spatially separated from it by an integer quantum Hall state. Near a resonance, the physics at energy scales below the level…
Fractional quantum Hall states at a half-filled Landau level are believed to carry an integer number $\mathcal{C}$ of chiral Majorana edge modes, reflected in their thermal Hall conductivity. We show that this number determines the primary…
We show that two intriguing features of mesoscopic transport, namely the modulation of Coulomb blockade peak-heights and the transmission phase-lapses occurring between subsequent peaks, are closely related. Our analytic arguments are…
We study the trapping of Abelian anyons (quasiholes and quasiparticles) by a local potential (e.g., induced by an AFM tip) in a microscopic model of fractional quantum Hall liquids with long-range Coulomb interaction and edge confining…
We develop a formalism to describe quasihole condensates in quantum Hall liquids and thereby extend the conformal field theory approach to the full hierarchy of spin-polarized Abelian states, and to several classes of non-Abelian…
The abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-abelian states emanating from the {\nu} = 5/2 Moore-Read state in the second Landau…
We discuss transport experiments for various non-Abelian quantum Hall states, including the Read-Rezayi series and a paired spin singlet state. We analyze the signatures of the unique characters of these states on Coulomb blockaded…
The semi-classical study of the integer Quantum Hall conductivity is investigated for electrons in a bi-periodic potential $V(x,y)$. The Hall conductivity is due to the tunnelling effect and we concentrate our study to potentials having…
We propose a phenomenological model that describes counterflow and drag experiments with quantum Hall bilayers in a \nu_T=1 state. We consider the system consisting of statistically distributed areas with local total filling factors…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
Starting from Laughlin type wave functions with generalized periodic boundary conditions describing the degenerate groundstate of a quantum Hall system we explictly construct $r$ dimensional vector bundles. It turns out that the filling…