High Landau levels in a smooth random potential for two-dimensional electrons

Raǐkh, M. É.; Shahbazyan, Tigran V.

doi:10.1103/physrevb.47.1522

Cited by 121 publications

(138 citation statements)

References 33 publications

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“…2), We turn now to the opposite limit of fully separated LLs, when the LL width 2Γ = 2(2ω c /πτ s,0 ) 1/2 [11] is small compared to ω c . This calculation can be done either by using Eqs.…”

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confidence: 99%

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Cyclotron-Resonance Harmonics in the ac Response of a 2D Electron Gas with Smooth Disorder

2003

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The frequency-dependent conductivity σxx(ω) of 2D electrons subjected to a transverse magnetic field and smooth disorder is calculated. The interplay of Landau quantization and disorder scattering gives rise to an oscillatory structure that survives in the high-temperature limit. The relation to recent experiments on photoconductivity by 76.40.+b The magnetotransport properties of a high-mobility 2D electron gas (2DEG) in semiconductor heterostructures are of great importance from the point of view of both fundamental physics and applications. Important information about the dynamical and spectral properties of the system is provided by its response to a microwave field. Within the quasiclassical Boltzmann theory, the dissipative ac conductivity σ xx (ω) = σ + (ω) + σ − (ω) of a non-interacting 2DEG in a magnetic field B is given by the Drude formula (we neglect spin for simplicity),where v F is the Fermi velocity, ν 0 = m/2π (withh = 1) the density of states (DOS), τ tr,0 the transport relaxation time at B = 0, ω c = eB/mc the cyclotron frequency, and m is the electron effective mass. For a sufficiently clean sample, ωτ tr,0 ≫ 1, Eq.(1) predicts a sharp cyclotron resonance (CR) peak at ω c = ω. It has been shown by Ando [1,2] that the Landau quantization of the orbital electron motion leads, in combination with disorder, to the emergence of harmonics of the CR at ω = nω c , n = 2, 3, . . .. Indeed, such a structure was experimentally observed [3]. The analytical calculations of Ref.[1] were performed, however, only for fully separated Landau levels with point-like scatterers [4].Very recently, great interest in the transport properties of a 2DEG in a microwave field has been caused by experiments on photoconductivity of exceptionally-highmobility samples by Zudov et al. [5] and Mani et al. [6], where oscillations controlled by the ratio ω/ω c were observed. Remarkably, these oscillations persisted down to magnetic fields as low as B ∼ 10 mT, an order of magnitude smaller than the field at which the Shubnikov-de Haas oscillations were damped. The experiments [5,6] triggered an outbreak of theoretical activity. Durst et al. [7] proposed (see also Refs. [8,9]) that the oscillations are governed by the following mechanism: an electron is excited by absorbing a photon with energy ω close to nω c and is scattered by disorder. In view of the oscillatory structure of the DOS, this leads to an extra contribution to the dc conductivity. In fact, a very similar mechanism of oscillatory photoconductivity was proposed long ago [10] for the case of a strong dc electric field.While the proposal of Ref.[7] is very appealing, calculations presented there involve a number of assumptions and approximations, which complicates a comparison with experiment. First, the consideration of Ref. [7] is restricted to the case of white-noise disorder with τ tr,0 = τ s,0 , where τ s,0 is the single-particle relaxation time at B = 0. On the other hand, the experiments are performed on high-mobility samples with smooth disorder, τ tr,0 /τ ...

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“…We will treat disorder within the self-consistent Born approximation (SCBA) [2], which is justified provided the disorder correlation length satisfies d ≪ l B and d ≪ v F τ s,0 , where l B = (c/eB) 1/2 is the magnetic length [11]. The Green function in the Landau level (LL) representation,…”

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confidence: 99%

Cyclotron-Resonance Harmonics in the ac Response of a 2D Electron Gas with Smooth Disorder

2003

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“…The inverse scattering time 1/ E E t( ) | Im ( )|/ = S D in the self-consistent Born approximation (SCBA) was found to be proportional to the total DOS [19][20][21]. Accordingly, the relation N E /N ( ) ( ) 0 = = t t 0 / E ( ) holds, where t 0 is the intralayer scattering time [22,23].…”

Section: Incoherent Interlayer Electron Hopping As a Possible Reason mentioning

confidence: 99%

Incoherent interlayer electron hopping as a possible reason for enhanced magnetic quantum oscillations in the mixed state of a layered organic superconductor

Gvozdikov

Wosnitza

2006

Low Temperature Physics

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We present a theory which is able to explain enhanced magnetic quantum-oscillation amplitudes in the superconducting state of a layered organic metal with incoherent electronic transport across the layers. The incoherence acts through the deformation of the layer-stacking factor which becomes complex and decreases the total scattering rate in the mixed state. This novel mechanism restores the coherence by establishing a long-range order across the layers and can compensate the usual decrease of the Dingle factor below the upper critical magnetic field caused by the intralayer scattering.

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“…For R = 0 (no reservoir) and χ 0 ≤ 2, this equation leads to the absence of states between the Landau levels. This unphysical result [3,4] is avoided as soon as R = 0. Assuming the value R = 5 necessary for suppressing significantly the chemical potential oscillations [12], we found [7] that the oscillations of χ(ε) are of the order of 10 % for H = 60 T, and thus neglected them in our numerical calculation [7] (i.e.…”

Section: Maxima Of Magnetoresistivitymentioning

confidence: 99%

“…In high magnetic fields, the oscillations of Γ(ε) become very strong. In such a regime, the mere consideration of point-like impurities has been shown to be inappropriate to describe correctly the magnetic quantum oscillations [3,4]. To our knowledge, the complete and satisfactory theory of the impurities effects on magnetic quantum oscillations, i.e.…”

Section: Introductionmentioning

confidence: 99%

Giant quantum oscillations of the longitudinal magnetoresistance in quasi-two-dimensional metals

Champel

Минеев

2004

Physica B: Condensed Matter

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We have investigated in frame of the quantum transport theory the magnetic quantum oscillations of the longitudinal magnetoresistance ρzz in quasi two-dimensional metals for a magnetic field perpendicular to the layers. Giant Shubnikov-de Haas oscillations are found when the cyclotron energyhωc is much larger than the interlayer transfer integral t (the two-dimensional limit). In large magnetic fields and at low temperatures, the minima of the magnetoconductivity σzz = ρ −1 zz exhibit a thermally activated behavior in presence of negligibly small chemical potential oscillations, as observed in the organic layered conductor β ′′ −(BEDT − TTF) 2 SF5CH2CF2SO3. The questions concerning the absence of strong chemical potential oscillations in such compound and the impurity self-energy are discussed.

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High Landau levels in a smooth random potential for two-dimensional electrons

Cited by 121 publications

References 33 publications

Cyclotron-Resonance Harmonics in the ac Response of a 2D Electron Gas with Smooth Disorder

Cyclotron-Resonance Harmonics in the ac Response of a 2D Electron Gas with Smooth Disorder

Incoherent interlayer electron hopping as a possible reason for enhanced magnetic quantum oscillations in the mixed state of a layered organic superconductor

Giant quantum oscillations of the longitudinal magnetoresistance in quasi-two-dimensional metals

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