Correlation Lengths of the Wigner-Crystal Order in a Two-Dimensional Electron System at High Magnetic Fields

Ye, P. D.; Engel, L. W.; Tsui, D. C.; Lewis, Rupert; Pfeiffer, L. N.; West, K. W.

doi:10.1103/physrevlett.89.176802

Cited by 106 publications

(30 citation statements)

References 29 publications

(49 reference statements)

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“…systems, 30 the presence of disorder may "pin" the order and allow finite grain-size Wigner crystallites at much higher n s . 31 Thus, in conclusion, the effects of the many-body Coulomb potential appear to manifest in a novel metallic phase in dilute mesoscopic 2DESs, with giant thermopower that decreases linearly as T → 0. While we cannot rule out the possibility that the system turns insulating at even lower T , the fact that it persists down to lowest experimental n s explored here indicates that the metallic phase might be the true ground state of strongly interacting 2DESs.…”

Section: Discussionmentioning

confidence: 96%

Unconventional metallicity and giant thermopower in a strongly interacting two-dimensional electron system

et al. 2012

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We present thermal and electrical transport measurements of low-density (10 14 m −2 ), mesoscopic twodimensional electron systems (2DESs) in GaAs/AlGaAs heterostructures at sub-Kelvin temperatures. We find that even in the supposedly strongly localized regime, where the electrical resistivity of the system is two orders of magnitude greater than the quantum of resistance h/e 2 , the thermopower decreases linearly with temperature indicating metallicity. Remarkably, the magnitude of the thermopower exceeds the predicted value in noninteracting metallic 2DESs at similar carrier densities by over two orders of magnitude. Our results indicate a new quantum state and possibly a novel class of itinerant quasiparticles in dilute 2DESs at low temperatures where the Coulomb interaction plays a pivotal role.

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Section: Discussionmentioning

confidence: 96%

Unconventional metallicity and giant thermopower in a strongly interacting two-dimensional electron system

et al. 2012

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“…More recent measurements have systematically investigated the form and location of the long wavelength magnetophonon resonance as a function of filling fraction, electron density, disorder and temperature [19][20][21][22][23][24], and have also found collective vibrational modes in the immediate vicinity of quantum Hall phases [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Theory of collective magnetophonon resonance and melting of a field-induced Wigner solid

et al. 2019

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Electron solid phases of matter are revealed by characteristic vibrational resonances.Sufficiently large magnetic fields can overcome the effects of disorder, leading to a weakly pinned collective mode called the magnetophonon. Consequently, in this regime it is possible to develop a tightly constrained hydrodynamic theory of pinned magnetophonons.The behavior of the magnetophonon resonance across thermal and quantum melting transitions has been experimentally characterized in two-dimensional electron systems.Applying our theory to these transitions we explain several key features of the data: (i) violation of the Fukuyama-Lee sum rule as the transition is approached is directly tied to the non-Lorentzian form taken by the resonance and (ii) the non-Lorentzian shape is caused by characteristic dissipative channels that become especially important close to melting: proliferating dislocations and uncondensed charge carriers. arXiv:1904.04872v1 [cond-mat.mes-hall]

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“…These resonances are interpreted as arising from shear modes of WC domains pinned by disorder and, consequently, as a manifestation of a finite shear modulus 3,10,14 , a distinguishing feature of a solid. We use nuclear magnetic resonance (NMR) to demonstrate another defining feature of a solid related to its structural properties.…”

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NMR profiling of quantum electron solids in high magnetic fields

et al. 2014

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When the motion of electrons is restricted to a plane under a perpendicular magnetic field, a variety of quantum phases emerge at low temperatures, the properties of which are dictated by the Coulomb interaction and its interplay with disorder. At very strong magnetic field, the sequence of fractional quantum , which reflect the mechanical properties characteristic of a solid. However, the most direct manifestation of the broken translational symmetry accompanying the solidification-the spatial modulation of particles' probability amplitudes-has not been observed yet. Here, we demonstrate that nuclear magnetic resonance provides a direct probe of the density topography of electron solids in the integer and fractional quantum Hall regimes. The data uncover quantum and thermal fluctuations of lattice electrons resolved on the nanometre scale. Our results pave the way to studies of other exotic phases with non-trivial spatial spin/charge order.Wigner crystallization is a concept originally proposed to occur in a disorder-free dilute electron system at zero magnetic field, when the Coulomb energy dominates over the kinetic energy 2 . Application of a strong perpendicular magnetic field (B) on a two-dimensional electron system (2DES) also facilitates Wigner crystallization [12][13][14][15] , as it quantizes the electron energy into a discrete spectrum known as Landau levels (LLs) and thereby quenches the kinetic energy. As the electrons are confined to orbits with spatial extent of the order of the magnetic length B = (h/2πeB) 1/2 (e: elementary charge, h: Planck's constant), Wigner crystallization becomes governed not by the electron density n, but by the LL filling factor ν = nh/eB(= 2πn B 2 ). Evidence for the formation of Wigner crystal (WC) domains in the regime of integer 16,17 and fractional 10,11 ν is provided by the observation of resonances in the microwave conductivity. These resonances are interpreted as arising from shear modes of WC domains pinned by disorder and, consequently, as a manifestation of a finite shear modulus 3,10,14 , a distinguishing feature of a solid. We use nuclear magnetic resonance (NMR) to demonstrate another defining feature of a solid related to its structural properties. The Knight shift measures the effective magnetic field that electron spins exert on the nuclei of the host material 18 , making it a sensitive probe of the local electron density and its spatial modulation.We studied a 2DES confined to a 27-nm-wide GaAs quantum well using a resistively detected NMR (RD-NMR) technique 19 in the millikelvin regime (Methods). Figure 1a shows resonance spectra of 75 As nuclei at B = 6.4 T, obtained at various filling factors around ν = 2, accessed using a gate voltage. At ν = 2, equal numbers of spinup and spin-down electrons fill the lowest N = 0 LL, resulting in zero net spin polarization. The corresponding resonance spectrum thus represents the bare resonance frequency of the 75 As nuclei, which is unaffected by the electron spin. As we move away from ν = 2, the addition of spin-...

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Correlation Lengths of the Wigner-Crystal Order in a Two-Dimensional Electron System at High Magnetic Fields

Cited by 106 publications

References 29 publications

Unconventional metallicity and giant thermopower in a strongly interacting two-dimensional electron system

Unconventional metallicity and giant thermopower in a strongly interacting two-dimensional electron system

Theory of collective magnetophonon resonance and melting of a field-induced Wigner solid

NMR profiling of quantum electron solids in high magnetic fields

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