Wave Function Spectroscopy in Quantum Wells with Tunable Electron Density

Salis, G.; Graf, Basile; Ensslin, Klaus; Campman, K. L.; Maranowski, K. D.; Gossard, A. C.

doi:10.1103/physrevlett.79.5106

Cited by 46 publications

(36 citation statements)

References 12 publications

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“…At a temperature of 100 mK and zero gate voltages the electron mobility is 16 m 2 /Vs and N s = 3.3 × 10 15 m −2 . While we have investigated many similar samples in the past [6,7,8,9,10] …”

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confidence: 99%

Two-subband quantum Hall effect in parabolic quantum wells

et al. 2006

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The low-temperature magnetoresistance of parabolic quantum wells displays pronounced minima between integer filling factors. Concomitantly the Hall effect exhibits overshoots and plateau-like features next to well-defined ordinary quantum Hall plateaus. These effects set in with the occupation of the second subband. We discuss our observations in the context of single-particle Landau fan charts of a two-subband system empirically extended by a density dependent subband separation and an enhanced spin-splitting g ⋆ . PACS numbers:At low temperatures a two-dimensional electron gas subject to a perpendicular magnetic field gives rise to the integer quantum Hall effect [1]. The Hall effect takes on quantized values ρ xy = h/e 2 ν around magnetic fields B = N s h/eν, with the integer filling factor ν counting the number of occupied Landau levels and N s being the carrier density. In these plateau regions of ρ xy the magnetoresistance ρ xx is exponentially suppressed. Each Landau level is described by a Landau level quantum number n = 0, 1, 2, . . ., a spin quantum number s = ±1/2 and a subband or well index i if several subbands in a quantum well are occupied or a double well system is investigated.Zhang et al.[2] have reported measurements on a quantum well system where the occupation of a second subband leads to additional maxima and minima in ρ xx between integer filling factors, accompanied by over-and undershoots of ρ xy . Here we report similar results obtained on parabolic quantum wells in which the subband occupation can be controlled by front and back gate voltages. We find that the observed phenomena can be qualitatively accounted for using an effective single-particle model where interaction effects beyond the mean field Hartree and exchange interactions are neglected. Previous experiments on double wells showed additional minima as well as hysteretic behavior (see Ref.[3] for a review) which was attributed to more subtle interaction effects [4,5].Our samples are 100 nm wide parabolic Al x Ga 1−x As quantum wells with the Al-content varying from x = 0.4 at the edges to x = 0 in the center of the parabola. Hall bars with Ohmic contacts were fabricated. A Schottky front gate and a back gate [10] allows to tune the electron sheet density N s and with it the number of occupied subbands. At a temperature of 100 mK and zero gate voltages the electron mobility is 16 m 2 /Vs and N s = 3.3 × 10 15 m −2 . While we have investigated many similar samples in the past [6,7,8,9,10]

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Section: Pacs Numbersmentioning

confidence: 99%

Two-subband quantum Hall effect in parabolic quantum wells

et al. 2006

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“…The difference between the two lowest subband energies reaches a minimum when the wave functions are centered with respect to the spike. Therefore, the minimum in n 1 provides the reference for the location of the wave functions in growth direction [12], where ∆z = 0.…”

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Variation of elastic scattering across a quantum well

et al. 1999

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The Drude scattering times of electrons in two subbands of a parabolic quantum well have been studied at constant electron sheet density and different positions of the electron distribution along the growth direction. The scattering times obtained by magnetotransport measurements decrease as the electrons are displaced towards the well edges, although the lowest-subband density increases. By comparing the measurements with calculations of the scattering times of a two-subband system, new information on the location of the relevant scatterers and the anisotropy of intersubband scattering is obtained. It is found that the scattering time of electrons in the lower subband depends sensitively on the position of the scatterers, which also explains the measured dependence of the scattering on the carrier density. The measurements indicate segregation of scatterers from the substrate side towards the quantum well during growth.The striking success of Ga [Al]As semiconductor heterostructures originates from the extremely high mobilities obtained in these materials. One key ingredient for the fabrication of such samples is modulation doping, where dopants and electrons are spatially separated. At low temperatures, impurity scattering, alloy scattering and interface roughness scattering limit the electron mobility [1]. If more than one subband is occupied, intersubband scattering takes place in addition [2,3].Information on the relevant scattering processes is usually obtained by measuring how quantum (τ q ) and Drude scattering times (τ ) vary with carrier density n S . For two-dimensional electron gases (2DEGs) realized in AlGaAs heterostructures, it is found that impurity scattering is dominant. In this case, one finds τ ∝ n γ S , with γ between 1 and 1.5, depending on the distance between the dopants and the 2DEG [1].In a two-subband system with subband densities n 1 and n 2 , the Drude scattering times τ i of subband i are usually found to increase monotonically with n i [4,5]. Recent results show that in a parabolic quantum well (PQW), τ 1 may also slowly decrease, i.e. γ < 0, when a second subband is occupied [6]. In this paper, we investigate this unusual dependence and show that it may be due to a certain arrangement of the ionized impurities.The PQW, grown by molecular beam epitaxy (MBE), is a 760Å wide Al x Ga 1−x As layer with x varying parabolically between 0 and 0.1 [7] (inset of Fig. 1a). In the center of the well, a three monolayer thick Al 0.05 Ga 0.95 As layer forms a potential spike. The well is embedded symmetrically in 200Å of undoped Al 0.3 Ga 0.7 As spacer layers and remote Si-doping layers on both sides. On the surface side, the donors are provided by 11 sheets, each with a Si donor density of nominally 5·10 15 m −2

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“…This is in oposition to the initial supositions of delta like perturbative spikes [1,2], but provide a strong support to the imaging using AFM induced perturbations, where the exact form and extension of the depletion underneath the tip are not so clearly controled. We believe that our results open new possibilities to the imaging experiments carried out so far on single quantum point contacts [8].…”

Section: Final Remarksmentioning

confidence: 99%

“…In other words, such mapping rely on measurements performed on different samples, each one probing the wave function at a designed position. Later on, Salis and coworkers [2] performed a wave function spectroscopy on a single parabolic quantum well, where the electron distribution was displaced with respect to a fixed perturbative barrier by applying an electric field. The energy shifts were obtained now by magnetotransport measurements.…”

Section: Introductionmentioning

confidence: 99%

Wave-function mapping conditions in open quantum dot structures

Mendoza

Schulz

2003

Phys. Rev. B

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We discuss the minimal conditions for wave function spectroscopy, in which resonant tunneling is the measurement tool. Two systems are addressed: resonant tunneling diodes, as a toy model, and open quantum dots. The toy model is used to analyze the crucial tunning between the necessary resolution in current-voltage characteristics and the breakdown of the wave functions probing potentials into a level splitting characteristic of double quantum wells. The present results establish a parameter region where the wavefunction spectroscopy by resonant tunneling could be achieved. In the case of open quantum dots, a breakdown of the mapping condition is related to a change into a double quantum dot structure induced by the local probing potential. The analogy between the toy model and open quantum dots show that a precise control over shape and extention of the potential probes is irrelevant for wave function mapping. Moreover, the present system is a realization of a tunable Fano system in the wave function mapping regime. PACS number(s) 73.40.Gk,73.21.Fg,73.21.La

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Wave Function Spectroscopy in Quantum Wells with Tunable Electron Density

Cited by 46 publications

References 12 publications

Two-subband quantum Hall effect in parabolic quantum wells

Two-subband quantum Hall effect in parabolic quantum wells

Variation of elastic scattering across a quantum well

Wave-function mapping conditions in open quantum dot structures

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