Related papers: Anyons in integer quantum Hall magnets
The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Here, we construct a new type of fractional quantum Hall system, which has the special property that it lives in…
In search of states with non-Abelian statistics, we explore the fractional quantum Hall effect in a system of two-dimensional charge carrier holes. We propose a new method of mapping states of holes confined to a finite width quantum well…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
Recently, in certain flat band lattice systems at commensurate fillings, fractional quantum Hall states have been found -- which have anyonic excitations. We study such systems away from commensuration, i.e. the ground state of an anyon gas…
The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both…
A theory of the static electron polarizability of crystals whose energy spectrum is modified by quantizing magnetic fields is presented. It is argued that The polarizability is strongly affected by non-dissipative Hall currents induced by…
Recent work has shown that the low energy sector of certain quantum Hall states is adiabatically connected to simple charge-density-wave patterns that appear, e.g., when the system is deformed into a thin torus. Here it is shown that the…
The fractional quantum Hall effect is a very particular manifestation of electronic correlations in two-dimensional systems in a strong perpendicular magnetic field. It arises as a consequence of a strong Coulomb repulsion between electrons…
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…
The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may…
One of the profound consequences of the fractional quantum Hall (FQH) effect is the notion of fractionally charged anyons. In spite of extensive experimental study, puzzles remain, however. For example, both shot-noise and Aharonov-Bohm…
The possibility of realizing fractional quantum Hall liquids in photonic systems has attracted a great deal of interest of late. Unlike electronic systems, interactions in photonic systems must be engineered from non-linear elements and are…
The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest…
We experimentally study electron transport between edge states in the fractional quantum Hall effect regime. We find an anomalous increase of the transport across the 2/3 incompressible fractional stripe in comparison with theoretical…
It has been shown that different Abelian and non-Abelian fraction quantum Hall states can be characterized by patterns of zeros described by sequences of integers {S_a}. In this paper, we will show how to use the data {S_a} to calculate…
A general mechanism is presented by which topological physics arises in strongly correlated systems without flat bands. Starting from a charge transfer insulator, topology emerges when the charge transfer energy between the cation and anion…
I review why and how physical states with fractional quantum numbers can occur, emphasizing basic mechanisms in simple contexts. The general mechanism of charge fractionalization is the passage from states created by local action of fields…
Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many--particle configuration space. Electron-magnetic field and electron-electron interactions…
The magnetotransport of a high-mobility two-dimensional electron gas coupled to a hovering split-ring resonator with controllable distance is studied in the quantum Hall regime. The measurements reveal an enhancement by more than a factor 2…
We predict the emergence a state of matter with intertwined ferromagnetism, charge order and topology in fractionally filled moir\'e superlattice bands. Remarkably, these quantum anomalous Hall crystals exhibit a quantized integer Hall…