Fractional Quantum Hall Effect at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math>in Hole Systems Confined to GaAs Quantum Wells

Liu, Yang; Graninger, A. L.; Hasdemir, S.; Shayegan, M.; Pfeiffer, L. N.; West, K. W.; Baldwin, K. W.; Winkler, Roland

doi:10.1103/physrevlett.112.046804

Cited by 31 publications

(36 citation statements)

References 27 publications

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“…Level crossings are of critical importance, especially since novel fractional quantum Hall states with even denominator have been shown to appear at such crossings in recent experiments 46,47 . We note that experimental observation of Landau levels for holes in photoluminescence measurements also reveals crossings 48 .…”

Section: Energy Spectra: Numerical Resultsmentioning

confidence: 99%

Magnetic field spectral crossings of Luttinger holes in quantum wells

Simion

Lyanda-Geller

2014

Phys. Rev. B

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We develop an analytic approach to two-dimensional (2D) holes in a magnetic field that allows us to gain insight into physics of measuring the parameters of holes, such as cyclotron resonance, Shubnikov-De Haas effect and spin resonance. We derive hole energies, cyclotron masses and the g-factors in the semiclassical regime analytically, as well as analyze numerical results outside the semiclassical range of parameters, qualitatively explaining experimentally observed magnetic field dependence of the cyclotron mass. In the semiclassical regime with large Landau level indices, and for size quantization energy much bigger than the cyclotron energy, the cyclotron mass coinsides with the in-plane effective mass, calculated in the absence of a magnetic field.The hole g-factor in a magnetic field perpendicular to the 2D plane is defined not only by the constant of direct coupling of the angular momentum of the holes to the magnetic field, but also by the Luttinger constants defining the effective masses of holes. We find that the g-factor for quasi 2D holes with heavy mass in the [001] growth direction in GaAs quantum well is g = 4.05 in the semiclasssical regime. Outside the semiclassical range of parameters, holes behave as a species completely different from electrons. Spectra for size-and magnetic-field-quantized holes are non-equidistant, not fan-like, and exhibit multiple crossings, including crossing in the ground level. We calculate the effect of Dresselhaus terms, which transform some of the crossings into anticrossings, and the effects of the anisotropy of the Luttinger Hamiltonian on the 2D hole spectra. Dresselhaus terms of different symmetries are taken into account, and a regularization procedure is developed for the k 3 z Dresselhaus terms. Control of the non-equidistant levels and crossing structure by the magnetic field can be used to control Landau level mixing in hole systems, and thereby control hole-hole interactions in the magnetic field.

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Section: Energy Spectra: Numerical Resultsmentioning

confidence: 99%

Magnetic field spectral crossings of Luttinger holes in quantum wells

Simion

Lyanda-Geller

2014

Phys. Rev. B

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“…The fractional quantum Hall effect (FQHE) states at half integer Landau fillings (ν) have long been of great interest [1][2][3][4][5][6][7][8], since they have correlations that differ from those of the fundamental Laughlin states found at odd denominators.…”

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confidence: 99%

“…At ν = 1/2 the FQHE has been observed in wide [1][2][3][4][5] or double quantum wells [8], and is ascribed to the two-component Halperin-Laughlin Ψ 331 state [9,10].…”

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confidence: 99%

Microwave spectroscopic observation of a Wigner solid within the ν=1/2 fractional quantum Hall effect

et al. 2017

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“…The incompressible state for holes persists in the entire range 1.4 < w < 2.2 including crossings of the ground odd and even n = 3 levels. The maximal gap occurs at w = 1.6, like in experiments [43]. For understanding correlations in an incompressible state, we calculate the many-body wavefunctions and density matrix, the topological entanglement entropy and the overlap with wavefunctions of model states.…”

mentioning

confidence: 85%

“…We examine whether the FQH state in experiments [43] is the 331 state. The Halperin 331 state arises for two species of interacting electrons.…”

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confidence: 99%

Non-Abelian ν=12 quantum Hall state in Γ8 valence band hole liquid

Simion

Lyanda-Geller

2017

Phys. Rev. B

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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 in a perpendicular magnetic field to states in a spherical shell geometry. This method provides single-particle hole states used in exact diagonalization of systems with a small number of holes in the presence of Coulomb interactions. An incompressible fractional quantum Hall state emerges in a hole liquid at the half-filling of the ground state in a magnetic field in the range of fields where single-hole states cross. This state has a negligible overlap with the Halperin 331 state, but a significant overlap with the Moore-Read Pfaffian state. Excited fractional quantum Hall states for small systems have sizable overlap with non-Abelian excitations of the Moore-Read Pfaffian state.Quasiparticles obeying non-Abelian statistics lead to fault tolerant quantum computing [1-3]. Exotic states resulting in non-Abelian excitations can arise in low dimensional quantum liquids in the presence of magnetic fields. The fractional quantum Hall (FQH) state in a twodimensional (2D) electron liquid at filling factor ν = 5/2 is the state most studied theoretically and possibly observed experimentally [4][5][6][7]. There are other FQH states at ν = 12/5 [8] and ν = 8/3 [8-10], bilayer ν = 1/2 2D electron phase [11][12][13][14], and ν = 1/4 state [15,16], for which non-Abelian origin of excitations has been discussed. Other candidates for non-Abelian systems are vortices in p-wave superconductors [17], and hybrid systems with proximity-induced s-wave superconductivity that mimic a p-wave pairing in semiconductors and topological insulators, due to spin-orbit coupling [18,19], Dirac spectra [20], or Laughlin anyon quasiparticles [21].

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Fractional Quantum Hall Effect atν=1/2in Hole Systems Confined to GaAs Quantum Wells

Cited by 31 publications

References 27 publications

Magnetic field spectral crossings of Luttinger holes in quantum wells

Magnetic field spectral crossings of Luttinger holes in quantum wells

Microwave spectroscopic observation of a Wigner solid within the ν=1/2 fractional quantum Hall effect

Non-Abelian ν=12 quantum Hall state in Γ8 valence band hole liquid

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