Two-Dimensional Magnetotransport in the Extreme Quantum Limit

Tsui, D. C.; Störmer, H. L.; Gossard, A. C.

doi:10.1103/physrevlett.48.1559

Cited by 4,463 publications

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“…The QHE takes place not only at integer fillings but also at fractional values as a result of electron correlation effects 135 . One successful model of the FQHE is based on 'composite fermions' , where the interaction energy is minimized by forming composite particles of electrons attached to a discrete number of magnetic flux quanta 136 .…”

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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Section: Quantum Computingmentioning

confidence: 99%

Emergent functions of quantum materials

2017

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“…T hirty years after the discovery of the celebrated fractional quantum Hall effect 1 , there are still open questions regarding electronic characteristics in this regime; one of them is the formation and nature of upstream chiral neutral modes. These modes, which carry energy without net charge [2][3][4][5][6][7][8][9][10] , are at the focus of recent experimental and theoretical studies, and are encouraged by the advent of the search for Majorana quasiparticles 11,12 .…”

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Extracting net current from an upstream neutral mode in the fractional quantum Hall regime

et al. 2012

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Upstream neutral modes, counter propagating to charge modes and carrying energy without net charge, had been predicted to exist in some of the fractional quantum Hall states and were recently observed via noise measurements. Understanding such modes will assist in identifying the wavefunction of these states, as well as shedding light on the role of Coulomb interactions within edge modes. Here, operating mainly in the n ¼ 2/3 state, we place a quantum dot a few micrometres upstream of an ohmic contact, which serves as a 'neutral modes source'. We show that the neutral modes heat the input of the dot, causing a net thermo-electric current to flow through it. Heating of the electrons leads to a decay of the neutral mode, manifested in the vanishing of the thermo-electric current at T4110 mK. This set-up provides a straightforward method to investigate upstream neutral modes without turning to the more cumbersome noise measurements.

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“…The integer QHE (q = 1) was discovered 10 years ago by von Klitzing, Dorda, and Pepper [1] in the two-dimensional electron gas (2DEG) confined to a Si Inversion layer. The fractional QHE (q > l and odd) was first observed by Tsui, Stornier, and Gossard [2] in the 2DEG at the interface of a Al a; Ga 1 _ ; j.As/GaAs heterostructure. Microscopically the two effects are entirely different.…”

Section: Introductionmentioning

confidence: 99%

Adiabatic Transport in the Fractional Quantum Hall Effect Regime

Beenakker

1991

Quantum Coherence in Mesoscopic Systems

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l IntroductionThe quantum Hall effect (QHE) is the phenomenon that the Hall conductance GH is quantized in units of e 2 /h, äs expressed by the formula G -?T ω (p and q being mutually prime integers). The integer QHE (q = 1) was discovered 10 years ago by von Klitzing, Dorda, and Pepper [1] in the two-dimensional electron gas (2DEG) confined to a Si Inversion layer. The fractional QHE (q > l and odd) was first observed by Tsui, Stornier, and Gossard [2] in the 2DEG at the interface of a Al a; Ga 1 _ ; j.As/GaAs heterostructure. Microscopically the two effects are entirely different. The integer QHE, on the one hand, can be explained satisfactorily in terms of the states of non-interacting electrons in a magnetic field (the Landau levels). The fractional QHE, on the other hand, exists only because of electron-electron interactions [3]. Phenomenologically, however, the integer and fractional QHE are quite similar. In an unbounded 2 DEG this similarity is understood from Laughlin's general argument [4] that: (1) The Hall conductance shows a plateau äs a function of magnetic field (or Fermi energy) whenever the quasi-particle excitations in the bulk of the 2 DEG are localized by disorder; and that: (2) The value of GH on the plateau is precisely an integer multiple p of ee*/h, where e* = e/q is the quasi-particle charge. (The product ee* appears because one e is needed to change the unit of conductance from Amperes per electron Volts to Amperes per Volts). Theory and experiment on the QHE in an unbounded 2 DEG have been reviewed in the books by Prange and Girvin [5] and by Chakraborty and Pietiläinen [6] (see also the article by MacDonald in the present volume).In the past few years, a variety of experiments have uncovered a novel phenomenology of the QHE on short length scales. For example, in small sub-micron-size samples

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Two-Dimensional Magnetotransport in the Extreme Quantum Limit

Cited by 4,463 publications

References 26 publications

Emergent functions of quantum materials

Emergent functions of quantum materials

Extracting net current from an upstream neutral mode in the fractional quantum Hall regime

Adiabatic Transport in the Fractional Quantum Hall Effect Regime

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