Many-body integer quantum Hall effect: Evidence for new phase transitions

Murphy, S. Q.; Eisenstein, J. P.; Boebinger, G. S.; Pfeiffer, L. N.; West, K. W.

doi:10.1103/physrevlett.72.728

Cited by 353 publications

(424 citation statements)

References 19 publications

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“…The experiments are complex and are frequently hard to interpret (and may require assumptions beyond the simplifying assumptions made in the current paper). While some of the experiments 17,18,19,20,21,22 point towards a continuous transition between two phases, it is not clear whether this could actually be a first order transition smeared by disorder. 8 There is no doubt, however, that a notable change of behavior takes place in the approximate vicinity of d/ℓ 0 ≈ 1.7 with ℓ 0 = φ 0 /B as the magnetic length.…”

Section: Introductionmentioning

confidence: 99%

“…1 While the nature of these two limiting states is reasonably well understood, the nature of the states at intermediate d is less understood and has been an active topic of both theoretical 3,5,6,7,8,9,10,11,12,13,14,15,16 and experimental interest. 17,18,19,20,21,22,23,24,25,26,27 Although there are many interesting questions remaining that involve more complicated experimental situations, within the current work we always consider a zero temperature bilayer system with zero tunnelling between the two layers and no disorder. Furthermore, we only consider the situation of ν = 1 2 + 1 2 where the electron density in each layer is such that n 1 = n 2 = B/(2φ 0 ) with φ 0 = hc/e the flux quantum and B the magnetic field.…”

Section: Introductionmentioning

confidence: 99%

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Trial wave functions forν=12+12quantum Hall bilayers

Möller¹,

Simon²,

Rezayi

2009

Phys. Rev. B

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Quantum Hall bilayer systems at filling fractions near ν = 1 2 + 1 2 undergo a transition from a compressible phase with strong intralayer correlation to an incompressible phase with strong interlayer correlations as the layer separation d is reduced below some critical value. Deep in the intralayer phase (large separation) the system can be interpreted as a fluid of composite fermions (CFs), whereas deep in the interlayer phase (small separation) the system can be interpreted as a fluid of composite bosons (CBs). The focus of this paper is to understand the states that occur for intermediate layer separation by using trial variational wavefunctions. We consider two main classes of wavefunctions. In the first class, previously introduced in Möller et al. (2003)] and generalizes the idea of pairing wavefunctions by allowing the CFs also to be replaced continuously by CBs. This generalization allows us to construct exceedingly good wavefunctions for interlayer spacings of d ℓ 0 , as well. The accuracy of the wavefunctions discussed in this work, compared with exact diagonalization, approaches that of the celebrated Laughlin wavefunction.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Trial wave functions forν=12+12quantum Hall bilayers

Möller¹,

Simon²,

Rezayi

2009

Phys. Rev. B

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“…Observation of steplike rise of conductivity, each step is due to discharge of a QD by a single photon, has been associated with the detection of a single photoexcited carrier in a single dot [6]. We propose here that, placed in a strong magnetic field, incident light on such a device would perhaps light up the quasiparticles of the incompressible state.Formally, our system is similar to a double-layer FQHE system [7,8], except that in one of the two layers electrons are confined by a harmonic potentialwhere ω 0 is the confinement potential strength and the corresponding oscillator length is l dot = (h/m * ω 0 ) 1 2 . We consider Coulomb interaction between the electrons in the dot and in the plane.…”

mentioning

confidence: 99%

“…Formally, our system is similar to a double-layer FQHE system [7,8], except that in one of the two layers electrons are confined by a harmonic potential…”

mentioning

confidence: 99%

Interaction of a quantum dot with an incompressible two-dimensional electron gas

Apalkov

Chakraborty

2002

Physica E: Low-dimensional Systems and Nanostructures

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We consider a system of a incompressible quantum Hall liquid in close proximity to a parabolic quantum dot containing a few electrons. We observe a significant influence of the interacting electrons in the dot on the excitation spectrum of the incompressible state in the electron plane. Our calculated charge density indicates that unlike in the case of an impurity, interacting electrons in the dot seem to confine the fractionally charged excitations in the incompressible liquid.A two-dimensional electron gas under the influence of a strong, external magnetic field exhibits the celebrated fractional quantum Hall effect (FQHE) [1,2], that has been the subject of intense investigation for almost two decades. One of the most successful description of the quantum state in such a system is the Laughlin state [3], which describes the ground state of an electron system with 1 3 -filled lowest Landau level, as a highly correlated incompressible liquid. Incompressibility of the state implies the existence of a gap in the excitation spectrum and that the low-lying elementary excitations are fractionally-charged quasiparticles and quasiholes [1][2][3]. A large body of theoretical and experimental work has already established many of these properties of the unique quantum state. Dispersion of various collective modes in the FQHE has also been well established [2].Quantum Hall (QH) properties of the electron gas, such as the ones mentioned above, are however for electron motion in a plane. On the other hand, when the electron motion in the plane is further quantized in the planar two dimensions, we get what is known as a quantum dot (QD) [4,5]. Quantum dots represent the ultimate reduction in the dimensionality of a semiconductor device where electrons have no kinetic energy and as a consequence, they have sharp energy levels like in atoms. These zero-dimensional electron systems have enjoyed enormous popularity because of their importance in understanding fundamental concepts of nanostructures and at the same time, for their application potentials. Development of extremely small self-assembled quantum dots (only a few nanometers across) containing only a few electrons that can be inserted into the dot in a controlled manner, have led to important new device applications. In this letter, we propose a system where a parabolic QD [4] containing only a few electrons is brought in close proximity to a two-dimensional electron gas (2DEG) that was initially in the Laughlin state with 1 3 filling of the lowest Landau level. We investigate the influence of interacting electrons in the dot on the Laughlin state that exists in the absence of the quantum dot.Why (and how) should one bring a quantum dot in the vicinity of a 2DEG? The answer is, a device similar to the type of system described here already exists as a singlephoton detector [6]. In this device, a layer of nanometersized InAs quantum dots is placed near a 2DEG, separated by a thin barrier. Charge carriers photoexcited by incident light (visible or near-infrared wavelengths)...

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“…In this case, a phase transition is induced in the system when 1 and 2 , respectively, are the Landau level filling factors in the two layers of the bilayer, sum up to give a total Landau level filling factor T ¼ 1 þ 2 ¼ 1; in addition, the layers must be sufficiently dilute (d=l B Շ1:8, where l B ¼ ðh=eBÞ 1=2 is the magnetic length 24 ). The two layers become highly correlated because the Fermi level lies in the middle of the lowest Landau level in each layer, making it possible to consider the layers as both made of electrons or of holes (quantum Hall bilayers, QHB).…”

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confidence: 99%

A complete laboratory for transport studies of electron-hole interactions in GaAs/AlGaAs ambipolar bilayers

Cumis

Waldie

Croxall

et al. 2017

Applied Physics Letters

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We present GaAs/AlGaAs double quantum well devices that can operate as both electron-hole (e-h) and hole-hole (h-h) bilayers, with separating barriers as narrow as 5 nm or 7.5 nm. With such narrow barriers, in the h-h configuration, we observe signs of magnetic-field-induced exciton condensation in the quantum Hall bilayer regime. In the same devices, we can study the zero-magnetic-field e-h and h-h bilayer states using Coulomb drag. Very strong e-h Coulomb drag resistivity (up to 10% of the single layer resistivity) is observed at liquid helium temperatures, but no definite signs of exciton condensation are seen in this case. Self-consistent calculations of the electron and hole wavefunctions show this might be because the average interlayer separation is larger in the e-h case than the h-h case.

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Many-body integer quantum Hall effect: Evidence for new phase transitions

Cited by 353 publications

References 19 publications

Trial wave functions forν=12+12quantum Hall bilayers

Trial wave functions forν=12+12quantum Hall bilayers

Interaction of a quantum dot with an incompressible two-dimensional electron gas

A complete laboratory for transport studies of electron-hole interactions in GaAs/AlGaAs ambipolar bilayers

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