Indications of a Luttinger liquid in the fractional quantum Hall regime

Milliken, F. P.; Umbach, C. P.; Webb, Richard A.

doi:10.1016/0038-1098(95)00181-6

Cited by 267 publications

(269 citation statements)

References 15 publications

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“…An experiment with high time resolution [10] has measured the propagation of a single chiral charge excitation for ν = 1/3 (m = 1 , p = 2), and ν = 2/3 (m = 2, p = 2); this is in agreement with the Jain theory, although the neutral excitations have not been seen yet. The resonant tunnelling experiment [12] has verified the conformal dimensions (2.41) for the simplest Laughlin fluid ν = 1/3 [13]. Extensions of this experiment to (m > 1) fluids have been suggested, as well as tests of the neutral edge spectrum [24].…”

Section: Methodsmentioning

confidence: 81%

“…The compositeness of the electron also plays a role in the resonant tunnelling experiment [12], in which two edges of the sample are pinched at one point, such that the corresponding edge excitations, having opposite chiralities, can interact. At ν = 1/3, the point interaction of two elementary anyons is relevant and determines the scaling law T 2/3 for the conductance [13].…”

Section: Non-abelian Fusion Rules and Non-abelian Statisticsmentioning

confidence: 99%

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Stable hierarchical quantum Hall fluids as W1+∞ minimal models

Cappelli¹,

Trugenberger

Zemba

1995

Nuclear Physics B

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In this paper, we pursue our analysis of the W 1+∞ symmetry of the lowenergy edge excitations of incompressible quantum Hall fluids. These excitations are described by (1 + 1)-dimensional effective field theories, which are built by representations of the W 1+∞ algebra. Generic W 1+∞ theories predict many more fluids than the few, stable ones found in experiments. Here we identify a particular class of W 1+∞ theories, the minimal models, which are made of degenerate representations only -a familiar construction in conformal field theory. The W 1+∞ minimal models exist for specific values of the fractional conductivity, which nicely fit the experimental data and match the results of the Jain hierarchy of quantum Hall fluids. We thus obtain a new hierarchical construction, which is based uniquely on the concept of quantum incompressible fluid and is independent of Jain's approach and hypotheses. Furthermore, a surprising non-Abelian structure is found in the W 1+∞ minimal models: they possess neutral quark-like excitations with SU (m) quantum numbers and nonAbelian fractional statistics. The physical electron is made of anyon and quark excitations. We discuss some properties of these neutral excitations which could be seen in experiments and numerical simulations.

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Section: Methodsmentioning

confidence: 81%

Section: Non-abelian Fusion Rules and Non-abelian Statisticsmentioning

confidence: 99%

Stable hierarchical quantum Hall fluids as W1+∞ minimal models

Cappelli¹,

Trugenberger

Zemba

1995

Nuclear Physics B

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“…Here, low-lying energy states can only prevail at the edge of the sample, and, concurrently, disperse linearly about the Fermi energy. Edge states can attain macroscopic linear (perimeter) extent, and the tunneling experiments between such states [182,114] have observed several features predicted theoretically [287,140]. We refer the interested reader to the review articles by Schulz et al [233] and Fisher and Glazman [98] for further details.…”

Section: Experimental Observations Of One-dimensional Luttinger Liquimentioning

confidence: 95%

Singular or non-Fermi liquids

2002

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“…No localization occurs and the residual * Electronic address: roddaro@sns.it disorder only affects the electrons giving a mere phase shift. These issues stimulated much experimental effort that provided striking indications of non-Fermi physics at work for edge-states in the fractional QH regime [7,8,9,10,11,12,13,14,15,16,17,18]. Many discrepancies and inconsistencies with the χLL description however remain and the validation of the Luttinger liquid model is still not conclusive.…”

mentioning

confidence: 99%

Quasi-particle tunneling at a constriction in a fractional quantum Hall state

Roddaro

Pellegrini

Beltram

2004

Solid State Communications

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Split-gate constrictions can be used to produce controllable scattering in a fractional quantum Hall state and constitute a very versatile model system for the investigation of non-Fermi physics in edge states. Controllable inter-edge tunneling can be achieved by tuning the constriction parameters and its out-of-equilibrium behavior can be explored as well. Here we review our results of tunneling non-linearities at a split-gate constriction in a wide range of temperatures and inter-edge coupling. The results are compared to available theoretical predictions of tunneling characteristics between Luttinger liquids. We show how partial agreement with these theoretical models is obtained in selected ranges of temperatures and inter-edge coupling, while striking deviations are obtained especially in the low-coupling, low-temperature regimes. A two-dimensional electron system (2DES) in the fractional quantum Hall (FQH) regime can give rise to many "exotic" phenomena driven by electron-electron interactions [1]. Under the application of a strong magnetic field and for peculiar ratios of the charge (n) and flux quanta (n φ = eB/h) densities the 2DES undergoes transitions to insulating Hall phases. For "magic" values of the fractional filling factor ν = n φ /n the ground state excitations are expected to be fractionally charged and to obey fractional statistics [2]. In both the integer and FQH effect, bulk states are characterized by an excitation gap while the only low-energy charged excitations propagate at the edge of the quantum Hall liquid thus creating a conducting, chiral one-dimensional (1D) channel. Wen predicted [3] that the edge of a FQH phase at ν = 1/q, where q is an odd integer, should be completely equivalent to a Luttinger liquid (LL) with interaction parameter g = ν. This peculiar model is known as chiral LL (χLL) and represents one of the simplest and most remarkable conceptual examples of a non-Fermi metal.The FQH edge state is not the only electronic system that is expected to support a non-fermionic behavior. In recent years, the experimental realization of a LL has become a target of several research efforts that also explored different fabrication strategies of condensed matter systems. In particular cleaved-edge overgrowth (CEO) was used to produce clean and long quantum wires: temperature power laws as well as resonant transport were measured and compared with LL predictions [4]. Finally carbon nanotubes are emerging as a promising model system for the verification of LL physics [5,6].Edge FQH states are expected to lead to a particularly robust realization of a LL: edge channels at ν = 1/q with q odd integer, in fact, can only propagate in one direction and do not suffer from backscattering by random impurities. No localization occurs and the residual * Electronic address: roddaro@sns.it disorder only affects the electrons giving a mere phase shift. These issues stimulated much experimental effort that provided striking indications of non-Fermi physics at work for edge-states in the fractional QH...

show abstract

Indications of a Luttinger liquid in the fractional quantum Hall regime

Cited by 267 publications

References 15 publications

Stable hierarchical quantum Hall fluids as W1+∞ minimal models

Stable hierarchical quantum Hall fluids as W1+∞ minimal models

Singular or non-Fermi liquids

Quasi-particle tunneling at a constriction in a fractional quantum Hall state

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