Hamiltonian theory of the composite-fermion Wigner crystal

Narevich, R.; Murthy, Ganpathy; Fertig, H. A.

doi:10.1103/physrevb.64.245326

Cited by 44 publications

(43 citation statements)

References 41 publications

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“…The results, together with other variational studies [27], supported the interpretation of the observed HFIPs and RIPs as pinned WCs. However, the liquid-WC transition phase diagram remains unsettled [28,29], especially in the range from ν=1 to the B=0 limit, since a reentrant WC that was expected at ν >1 (Ref. 26(b)) has never been observed experimentally.…”

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Connecting the Reentrant Insulating Phase and the Zero-Field Metal-Insulator Transition in a 2D Hole System

et al. 2012

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Connecting the Reentrant Insulating Phase and the Zero-Field Metal-Insulator Transition in a 2D Hole System

et al. 2012

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“…and as such is evidence for CF interaction. FQHEs of interacting CFs have been observed [6] as well, and CF Wigner solids have been considered theoretically [23][24][25] for low electron Landau fillings. Changing ν = 1/3 ± 0.015 to CF filling results in ν CF = 1 ± 0.15.…”

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Observation of a Pinning Mode in a Wigner Solid withν=1/3Fractional Quantum Hall Excitations

et al. 2010

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We report the observation of a resonance in the microwave spectra of the real diagonal conductivities of a two-dimensional electron system within a range of ∼ ±0.015 from filling factor ν = 1/3.The resonance is remarkably similar to resonances previously observed near integer ν, and is interpreted as the collective pinning mode of a disorder-pinned Wigner solid phase of e/3-charged carriers . * These authors contributed equally to this paper. Wigner solids occur in 2DES for small Landau level fillings (ν) [7][8][9], when the kinetic energy of carriers is quenched by the magnetic field, so that the carriers become effectively dilute, with their typical spacing larger than the magnetic length l B = (h/eB) 1/2 . At least for 2DES samples of extremely low disorder, Wigner solids can occur as well within the ranges of integer quantum Hall effect plateaus [10], in which there is a dilute population of electrons or holes in a partially filled Landau level, along with one or more completely filled Landau levels. Within the IQHE, Wigner solids are composed of carriers generated by moving ν away from its integer value, the insulating property of the pinned solid gives the quantized Hall plateau, which is concomitant with vanishing diagonal conductivity, its finite width.The pinning of the Wigner solid by residual disorder [11], besides causing them to be insulators and producing finite correlation lengths for crystalline order, gives rise to a striking rf or microwave resonance in the spectrum [10,[12][13][14][15][16]. This resonance is understood as a pinning mode, or a collective oscillation of solid domains within the disorder potential.Pinning modes [12] can be seen both in the low ν state [13][14][15], that terminates the FQHE series, and within IQHE's of samples with extremely low disorder [10,16]. This paper reports the observation of a microwave resonance within the ν range of the 1/3 FQHE. The resonance is interpreted as pinning mode of a Wigner solid of 1/3 charged excitations, and this interpretation is supported by a comparison of the parameters of the resonance near 1/3 with those of a pinning resonance observed near ν = 1 in the same sample.Both the resonance near ν = 1/3 and the resonance near ν = 1 show an increase of peak frequency, f pk , as quasiparticle charge density decreases, and the integrated absorptions 2 of both resonances suggest that much of the quasiparticle charge density is participating in the mode. The resonance around 1/3 occurs for fillings within ±0.015 of 1/3, much narrower than the ±0.16 range of resonance within the IQHE around ν = 1, and for the same quasiparticle number density,ñ, the resonance peak frequencies around 1 and 1/3 are nearly the same.The data presented are from a 2DES in a 50 nm wide GaAs/AlGaAs/GaAs quantum well (#7-20-99.1) with electron density n = 1.1 × 10 11 /cm 2 , and low temperature mobility µ = 15 × 10 6 cm 2 /Vs. The microwave spectroscopy technique is similar to those reported earlier [10,[12][13][14][15][16]. As illustrated in Fig. 1(a), we deposi...

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“…the actual ground state is a type-I CFWC. [10][11][12][13][14] Essentially, electrons capture fewer than the maximum number of vortices available to them, and use the remaining degrees of freedom to form a WC. The CFWC has been shown to be an excellent approximation of the exact state in numerical diagonalization studies.…”

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Static and dynamic properties of type-II composite fermion Wigner crystals

Archer

Jain

2011

Phys. Rev. B

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The Wigner crystal of composite fermions is a strongly correlated state of complex emergent particles in two dimensions, and therefore its unambiguous detection would be of significant importance. Recent observation of optical resonances in the vicinity of filling factor ν = 1/3 has been interpreted as evidence for a pinned Wigner crystal of composite fermions [Zhu et al., Phys. Rev. Lett. 105, 126803 (2010)]. We evaluate in a microscopic theory the shear modulus and the magnetophonon and magnetoplasmon dispersions of the composite fermion Wigner crystal in the vicinity of filling factors 1/3, 2/5, and 3/7. We determine the region of stability of the crystal phase, and also relate the frequency of its pinning mode to that of the corresponding electron crystal near integer fillings. These results are in good semiquantitative agreement with experiment, and therefore support the identification of the optical resonance as the pinning mode of the composite fermions Wigner crystal. Our calculations also bring out certain puzzling features, such as a relatively small melting temperature for the composite fermion Wigner crystal, and also suggest a higher asymmetry between Wigner crystals of composite fermion particles and holes than that observed experimentally.

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Hamiltonian theory of the composite-fermion Wigner crystal

Abstract: Experimental results indicating the existence of the high magnetic field Predictions for gaps and the shear modulus of the crystal are presented, and found to be in reasonable agreement with experiments.

Cited by 44 publications

References 41 publications

Connecting the Reentrant Insulating Phase and the Zero-Field Metal-Insulator Transition in a 2D Hole System

Connecting the Reentrant Insulating Phase and the Zero-Field Metal-Insulator Transition in a 2D Hole System

Observation of a Pinning Mode in a Wigner Solid withν=1/3Fractional Quantum Hall Excitations

Static and dynamic properties of type-II composite fermion Wigner crystals

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