Multiple Phases with the Same Quantized Hall Conductance in a Two-Subband System

Zhang, X. C.; Faulhaber, Donald Richard; Jiang, H. W.

doi:10.1103/physrevlett.95.216801

Cited by 42 publications

(52 citation statements)

References 17 publications

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“…4(f) is generally similar to the results of Ref. 2. We interpret a dip in the magnetoresistance as being related to a gap in the energy spectrum of the system.…”

Section: Pacs Numberssupporting

confidence: 76%

“…2. This indicates that the related gaps in the energy spectrum are smaller than the Landau gaphω c .…”

Section: Pacs Numbersmentioning

confidence: 94%

“…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.…”

Section: Pacs Numbersmentioning

confidence: 99%

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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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“…4(f) is generally similar to the results of Ref. 2. We interpret a dip in the magnetoresistance as being related to a gap in the energy spectrum of the system.…”

Section: Pacs Numberssupporting

confidence: 76%

“…2. This indicates that the related gaps in the energy spectrum are smaller than the Landau gaphω c .…”

Section: Pacs Numbersmentioning

confidence: 94%

Section: Pacs Numbersmentioning

confidence: 99%

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Two-subband quantum Hall effect in parabolic quantum wells

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“…In addition, the LL splittings appear as finer split lines in the SdHOs. For each LL crossing, there is an enhancement of ρ xx due to the enhanced density of states 20,21 , and each crossing point can be uniquely identified by B and ν.The positions of the crossings in B and ν space depend sensitively on the TLG band structure, and therefore enable an electronictransport determination of the relevant SWMcC parameters for TLG. These parameters, proposed to explain the band structure of graphite 10 , describe the different intra-and interlayer hopping terms in the different graphene sheets (Fig.…”

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confidence: 99%

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confidence: 99%

Quantum Hall effect and Landau-level crossing of Dirac fermions in trilayer graphene

et al. 2011

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The physics of Dirac fermions in condensed-matter systems has received extraordinary attention following the discoveries of two new types of quantum Hall effect in single-layer and bilayer graphene [1][2][3] . The electronic structure of trilayer graphene (TLG) has been predicted to consist of both massless single-layer-graphene-like and massive bilayer-graphene-like Dirac subbands [4][5][6][7] , which should result in new types of mesoscopic and quantum Hall phenomena. However, the low mobility exhibited by TLG devices on conventional substrates has led to few experimental studies 8,9 . Here we investigate electronic transport in high-mobility (>100,000 cm Bernal-or ABA-stacked TLG (Fig. 1b) is an intriguing material to study Dirac physics and the quantum Hall effect (QHE) because of its unique band structure, which, in the simplest approximation, consists of massless single-layer-graphene (SLG)-like and massive bilayer graphene (BLG)-like subbands at low energy (Fig. 1c;. The energies of the Landau levels (LLs) for massless charge carriers depend on the square root of the magnetic field √ B (refs 1, 2,11-13), whereas for massive charge carriers they depend linearly on B (refs 3,11,12,14). Therefore, the LLs from these two different subbands in TLG should cross at some finite fields, resulting in accidental LL degeneracies at the crossing points. However, one of the main challenges so far to observe the QHE in TLG has been its low mobility on SiO 2 substrates 8,9 . To overcome this problem, we use hexagonal boron nitride (hBN) single crystals 15 as local substrates, which have been shown to reduce carrier scattering in graphene devices 16 (See Methods and Supplementary Information for fabrication). Substrate-supported devices also enable us to reach higher carrier density than suspended samples 17 , which is necessary for the observation of the LL crossings. Figure 1e,f shows the resistivity and conductivity of a TLG device at zero magnetic field. The resistivity at the Dirac peak exhibits a strong temperature dependence, which in SLG is a strong indication of high device quality 18,19 . In addition, we also observe a doublepeak structure at low temperatures (Fig. 1e). This double-peak structure is probably due to the band overlap that occurs in TLG when all SWMcC parameters are included in the tight-binding calculation of its band structure, as we show below. The field-effect mobility of this device reaches 110,000 cm 2 V −1 s −1 at 300 mK at densities as high as 6 × 10 11 cm −2 . This mobility value is two orders of magnitude higher than previously reported values for supported TLG (refs 8,9) and comparable to suspended samples 17,19 . The low disorder and high mobility enable us to probe LL crossings of Dirac fermions through the measurement of Shubnikov-de Haas oscillations (SdHOs). Figure 2a shows longitudinal resistivity ρ xx as a function of 1/B, for a carrier density n = −4.4 × 10 12 cm −2 . At low B (below ∼1 T), there are a number of oscillations characterized by broad minima separated by relatively n...

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Ringlike structures in the density–magnetic‐field ρ _xx diagram of two‐subband quantum Hall systems

Ferreira¹,

Freire

Egues

2006

Phys. Status Solidi (c)

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Motivated by recent experiments [Zhang et al., Phys. Rev. Lett. 95, 216801 (2005) and Ellenberger et al., cond-mat/0602271] reporting novel ringlike structures in the density-magnetic-field (n2D-B) diagrams of the longitudinal resistivity ρ xx of quantum wells with two subbands, we investigate theoretically here the magneto-transport properties of these quantum-Hall systems. We determine ρ xx via both the Hartree and the Kohn-Sham self-consistent schemes plus the Kubo formula. While the Hartree calculation yields diamondshaped structures in the n 2D -B diagram, the calculation including exchange and correlation effects (KohnSham) more closely reproduces the ringlike structures in the experiments.

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Multiple Phases with the Same Quantized Hall Conductance in a Two-Subband System

Cited by 42 publications

References 17 publications

Two-subband quantum Hall effect in parabolic quantum wells

Two-subband quantum Hall effect in parabolic quantum wells

Quantum Hall effect and Landau-level crossing of Dirac fermions in trilayer graphene

Ringlike structures in the density–magnetic‐field ρ _xx diagram of two‐subband quantum Hall systems

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Multiple Phases with the Same Quantized Hall Conductance in a Two-Subband System

Cited by 42 publications

References 17 publications

Two-subband quantum Hall effect in parabolic quantum wells

Two-subband quantum Hall effect in parabolic quantum wells

Quantum Hall effect and Landau-level crossing of Dirac fermions in trilayer graphene

Ringlike structures in the density–magnetic‐field ρ xx diagram of two‐subband quantum Hall systems

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Product

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Ringlike structures in the density–magnetic‐field ρ _xx diagram of two‐subband quantum Hall systems