The hierarchy of incompressible fractional quantum Hall states

Quinn, John J.; Wójs, Arkadiusz; Yi, Kyung–Soo; Simion, George

doi:10.1016/j.physrep.2009.06.002

Cited by 18 publications

(9 citation statements)

References 159 publications

(320 reference statements)

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“…Throughout the extensive history of the fractional quantum Hall (FQH) effect, a lot has been learned about the elementary excitations above the ground state at FQH plateaus. In the continuum, numerous trial wave functions have been checked using numerical calculations [1,2] and the elementary excitations of them are well defined [3][4][5]. Moreover, Chern-Simons theories can be constructed for many common states and their elementary excitations can also be understood within this framework [6,7].…”

Section: Introductionmentioning

confidence: 99%

Abelian topological order of ν=2/5 and 3/7 fractional quantum Hall states in lattice models

2021

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Determining the statistics of elementary excitations supported by fractional quantum Hall states is crucial to understanding their properties and potential applications. In this paper, we use the topological entanglement entropy as an indicator of Abelian statistics to investigate the single-component =2/5 and 3/7 states for the Hofstadter model in the band mixing regime. We perform many-body simulations using the infinite cylinder density matrix renormalization group and present an efficient algorithm to construct the area law of entanglement, which accounts for both numerical and statistical errors. Using this algorithm, we show that the =2/5 and 3/7 states exhibit Abelian topological order in the case of two-body nearest-neighbor interactions. Moreover, we discuss the sensitivity of the proposed method and fractional quantum Hall states with respect to interaction range and strength.

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Section: Introductionmentioning

confidence: 99%

Abelian topological order of ν=2/5 and 3/7 fractional quantum Hall states in lattice models

2021

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“…The non-perturbative physics of bands within the lowest LL is understood as a consequence of the formation of composite fermions. The composite fermion (CF) theory [4][5][6] postulates a mapping of the problem of interacting electrons at filling factor ν into that of composite fermions at filling factor ν * , the two related by ν = ν * /(2pν * ± 1) where p is a positive integer. The underlying physics is that electrons capture 2p vortices each as a result of the repulsive interaction; this, in turn, produces a dynamics, due to the Berry phases produced by the bound vortices, as though composite fermions experienced a reduced magnetic field given by B * = B − 2pρφ 0 , where φ 0 = hc/e is the flux quantum.…”

Section: Introductionmentioning

confidence: 99%

State counting for excited bands of the fractional quantum Hall effect: Exclusion rules for bound excitons

2013

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Exact diagonalization studies have revealed that the energy spectrum of interacting electrons in the lowest Landau level splits, nonperturbatively, into bands, which is responsible for the fascinating phenomenology of this system. The theory of nearly free composite fermions has been shown to be valid for the lowest band, and thus to capture the low-temperature physics, but it overpredicts the number of states for the excited bands. We explain the state counting of higher bands in terms of composite fermions with an infinitely strong short-range interaction between an excited composite-fermion particle and the hole it leaves behind. This interaction, the form of which we derive from the microscopic composite-fermion theory, eliminates configurations containing certain tightly bound composite-fermion excitons. With this modification, the composite-fermion theory reproduces, for all well defined excited bands seen in exact diagonalization studies, an exact counting for ν > 1/3, and an almost exact counting for ν 1/3. The resulting insight clarifies that the corrections to the nearly free composite-fermion theory are not thermodynamically significant at sufficiently low temperatures, thus providing a microscopic explanation for why it has proved successful for the analysis of the various properties of the composite-fermion Fermi sea.

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“…Recent works 6,16 give insight on the correspondence between the observed PL emission shape at fractional and the energy spectrum, i.e., binding energies vs momentum, of the initial photoexcited system and of the final state after the recombination. Since the inhibition of the recombination is caused by localization and change in the screening response of the electron gas, 7 the smaller reduction in the PL intensity for the 4/5 and 5/7 states with respect to the adjacent 2/3 state can be attributed to the fact that the energy spectra of the initial or final states and the localization and screening response of the charges are more modified when the CFs undergo IQHE rather than FQHE.…”

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confidence: 99%

Optical detection of quantum Hall effect of composite fermions and evidence of theν=3/8state

et al. 2010

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In the photoluminescence spectra of a two-dimensional electron gas in the fractional quantum Hall regime we observe for the first time the states at filling factor =4/ 5, 5/7, 4/11, and 3/8 as clear minima in the emission peak intensity or area. The first three states are described as interacting composite fermions in fractional quantum Hall regime. The minimum in the intensity at =3/ 8, which is not explained within this picture, can be an evidence of a suppression of the screening of the coulomb interaction among the effective quasiparticles involved in this intriguing state.Several magnetotransport and magneto-optical studies have been realized on the two-dimensional electron gas ͑2DEG͒ created in a modulation-doped semiconductor quantum well, allowing the observation of the integer quantum Hall effect ͑IQHE͒ and fractional quantum Hall effect ͑FQHE͒. 1-4 Various theories, that envisage the formation of Landau levels ͑LLs͒ and composite fermions ͑CFs͒, have been proposed to explain these phenomena. 1-5 Many body interactions rule the arrangement of electrons in two dimensions placed in a high magnetic field, leading them to form highly correlated states. 1 The presence of residual disorder is a fundamental ingredient for the observation of these quantum effects. However, FQHE at fractional filling factors that cannot be explained as IQHE of CFs has been observed in transport experiments, 2 and not all the features observed in the photoluminescence ͑PL͒ experiments are well understood but they keep on producing sources of research and discussion. 6 In this work we report the first evidence in optical emission experiments of CFs in fractional quantum Hall regime at filling factors =4/ 5, 5/7, 4/11, and of the exotic state =3/ 8. In particular we analyze the intensity and the area of the 2DEG PL emission as a function of the magnetic field B, for filling factors down to 2/7. Using a model based on the CFs picture 5 and the coulomb screening of the 2DEG ͑Ref. 7͒ we explain the structures observed in the spectra at several fractional .The experiments were performed on a 20-nm-thick single sided modulation-doped GaAs/AlGaAs single quantum well with carrier density n = 1.8ϫ 10 11 cm −2 and mobility = 1.6ϫ 10 6 cm 2 V −1 s −1 measured at 1.5 K. Indium contacts were placed on the sample to allow simultaneous transport and optical experiments. The sample was placed in a dilution fridge and was excited at 1.748 eV with the light of a Ti:sapphire laser. We present the PL measurements at the temperatures of 590 and 35 mK, with laser excitation power lower than 400 W.In Fig. 1 we show the PL spectra at 590 mK as a function of B and we observe that the intensity of the emission, deriving from the recombination of the 2DEG electrons in their first Landau level L 0 with photocreated valence holes in their first LL, varies markedly as the magnetic field increases. For filling factors greater than 2, i.e., B smaller than 3.8 T ͑B =2 ͒, we observe the emission from the higher LLs, which are at higher energy with respect to the L ...

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The hierarchy of incompressible fractional quantum Hall states

Cited by 18 publications

References 159 publications

Abelian topological order of ν=2/5 and 3/7 fractional quantum Hall states in lattice models

Abelian topological order of ν=2/5 and 3/7 fractional quantum Hall states in lattice models

State counting for excited bands of the fractional quantum Hall effect: Exclusion rules for bound excitons

Optical detection of quantum Hall effect of composite fermions and evidence of theν=3/8state

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