Nonabelions in the fractional quantum hall effect

Moore, Gregory W.; Read, N.

doi:10.1016/0550-3213(91)90407-o

Cited by 2,889 publications

(3,959 citation statements)

References 45 publications

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“…FQH states, in particular the non-Abelian states, have been shown to be very useful as building blocks of a quantum computer 45,46 . A high-temperature non-Abelian quantum Hall states in the TMO heterostructures, for example, at ν = 1/2 filling where natural candidate states are in the same universality class of Pfaffian states 47 or anti-Pfaffian states 48,49 , if realized experimentally, would have strong impacts on both fundamental physics and its applications, including the efforts of realizing topological quantum computation.…”

Section: Resultsmentioning

confidence: 99%

Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures

et al. 2011

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Topological insulators are characterized by a non-trivial band topology driven by the spin-orbit coupling. To fully explore the fundamental science and application of topological insulators, material realization is indispensable. Here we predict, based on tight-binding modelling and first-principles calculations, that bilayers of perovskite-type transition-metal oxides grown along the [111] crystallographic axis are potential candidates for two-dimensional topological insulators. The topological band structure of these materials can be fine-tuned by changing dopant ions, substrates and external gate voltages. We predict that LaAuo 3 bilayers have a topologically non-trivial energy gap of about 0.15 eV, which is sufficiently large to realize the quantum spin Hall effect at room temperature. Intriguing phenomena, such as fractional quantum Hall effect, associated with the nearly flat topologically non-trivial bands found in e g systems are also discussed.

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Section: Resultsmentioning

confidence: 99%

Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures

et al. 2011

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“…This paired state is also present in the A-phase of superfluid 3 He, see e.g. [33], as well as arises for composite fermions in the theory of the fractional quantum Hall effect [34]. A spin-singlet chiral superconductor has, however, not yet been experimentally verified, and, at least in terms of a growing number of theoretical results, doped graphene seems to be a very promising candidate.…”

Section: Introductionmentioning

confidence: 99%

Chirald-wave superconductivity in doped graphene

Black‐Schaffer

Honerkamp

2014

J. Phys.: Condens. Matter

175

176

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Abstract. A highly unconventional superconducting state with a spin-singlet d x 2 −y 2 ± id xy -wave, or chiral d-wave, symmetry has recently been proposed to emerge from electron-electron interactions in doped graphene. Especially graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverges, has been argued to likely be a chiral d-wave superconductor. In this review we summarize the currently mounting theoretical evidence for the existence of a chiral d-wave superconducting state in graphene, obtained with methods ranging from mean-field studies of effective Hamiltonians to angle-resolved renormalization group calculations. We further discuss multiple distinctive properties of the chiral d-wave superconducting state in graphene, as well as its stability in the presence of disorder. We also review means of enhancing the chiral d-wave state using proximity-induced superconductivity. The appearance of chiral d-wave superconductivity is intimately linked to the hexagonal crystal lattice and we also offer a brief overview of other materials which have also been proposed to be chiral d-wave superconductors.

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“…Another possible candidate to realize Majorana fermions is in two-dimensional semiconductors showing the fractional quantum Hall effect (FQHE) or, more specifically, those which belong to a Moore-Read Pfaffian state 134 . The QHE takes place not only at integer fillings but also at fractional values as a result of electron correlation effects 135 .…”

Section: Quantum Computingmentioning

confidence: 99%

Emergent functions of quantum materials

2017

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Materials can harbour quantum many-body systems, most typically in the form of strongly correlated electrons in solids, that lead to novel and remarkable functions thanks to emergence-collective behaviours that arise from strong interactions among the elements. These include the Mott transition, high-temperature superconductivity, topological superconductivity, colossal magnetoresistance, giant magnetoelectric e ect, and topological insulators. These phenomena will probably be crucial for developing the next-generation quantum technologies that will meet the urgent technological demands for achieving a sustainable and safe society. Dissipationless electronics using topological currents and quantum spins, energy harvesting such as photovoltaics and thermoelectrics, and secure quantum computing and communication are the three major fields of applications working towards this goal. Here, we review the basic principles and the current status of the emergent phenomena and functions in materials from the viewpoint of strong correlation and topology.E mergence is a concept developed for many-body systems, indicating the properties, phenomena, and functions that never appear in the individual elements but are realized only when a huge number of elements get together 1 . Inside materials, emergent phenomena are often seen due to the interaction of electronic states; with recent developments on electronic states in solids schematically summarized in Fig. 1a. Electrons in solids have several degrees of freedom: charge, spin and orbital, and are characterized by the topological nature determined by the atomic potential on the crystal lattice structure, as schematically shown in Fig. 1b. These five attributes are coupled together and determine the overall responses to stimuli, which appear as materials' electrical, magnetic, optical, thermal, and mechanical properties.These collective electrons demonstrate various macroscopic quantum phenomena, the representative example of which is superconductivity. One of the big challenges in condensed matter physics is to increase the temperature (T c ) at which superconductivity can be observed to above room temperature. However, there are many other macroscopic quantum phenomena that are already observable above room temperature. One is magnetism (by the Bohr-van Leeuwen theorem), and the other is ferroelectricity 2,3 . Remarkably, there are common features of these three macroscopic quantum phenomena: the order parameter, which is of quantum origin, behaves as a classical quantity, and the quantum topology plays a crucial role.The topological nature of the electronic states is the key concept in the most recent developments in understanding quantum materials. The quantum Hall effect, topological insulators, and topological superconductors are all characterized by nontrivial topologies in Hilbert space. The Berry phase, which describes the connection and curvature of the subspace of Hilbert space, plays the central role in the unified principle to describe this topological nature 4 . ...

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Nonabelions in the fractional quantum hall effect

Cited by 2,889 publications

References 45 publications

Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures

Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures

Chirald-wave superconductivity in doped graphene

Emergent functions of quantum materials

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