Modulation of Landau levels by a one-dimensional periodic potential

Milton, B.; Emeleus, C. J.; Lister, Kevin; Davies, John H.; Long, A. R.

doi:10.1016/s1386-9477(99)00107-1

Cited by 12 publications

(23 citation statements)

References 8 publications

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“…Much of the above phenomenology has been thoroughly analyzed theoretically, by a variety of techniques including quantum mechanical approaches 5,6 involving diagrammatics 7,10,11 or solution of a quantum Boltzmann equation 8 , and quasiclassical approaches 2,3,4,12,13 . The experimental realization of these systems is also well advanced 1,2,5,6,14,16 with precise confirmation of the theoretical predictions already possible. So far however a theory for the influence of quantum interference processes in a periodic potential and high magnetic field has been missing.…”

Section: Introductionsupporting

confidence: 60%

Weak localization and integer quantum Hall effect in a periodic potential

Schwiete¹,

Taras-Semchuk²,

Efetov³

2003

Phys. Rev. B

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We consider magnetotransport in a disordered two-dimensional electron gas in the presence of a periodic modulation in one direction. Existing quasiclassical and quantum approaches to this problem account for Weiss oscillations in the resistivity tensor at moderate magnetic fields, as well as a strong modulation-induced modification of the Shubnikov-de Haas oscillations at higher magnetic fields. They do not account, however, for the operation at even higher magnetic fields of the integer quantum Hall effect, for which quantum interference processes are responsible. We introduce a field theory approach, based on a nonlinear σ model, which encompasses naturally both the quasiclassical and quantum mechanical approaches, as well as providing a consistent means of extending them to include quantum interference corrections. A perturbative renormalization-group analysis of the field theory shows how weak localization corrections to the conductivity tensor may be described by a modification of the usual one-parameter scaling, such as to accommodate the anisotropy of the bare conductivity tensor. We also show how the two-parameter scaling, conjectured as a model for the quantum Hall effect in unmodulated systems, may be generalized similarly for the modulated system. Within this model we illustrate the operation of the quantum Hall effect in modulated systems for parameters that are realistic for current experiments.

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Section: Introductionsupporting

confidence: 60%

Weak localization and integer quantum Hall effect in a periodic potential

Schwiete¹,

Taras-Semchuk²,

Efetov³

2003

Phys. Rev. B

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“…( 4)] was also reported for electrostatic ULSLs with a strong modulation amplitude induced by a patterned InGaAs stressor layer. 9 Interestingly, the authors observed that the trend is reversed at higher magnetic fields; the amplitude is enhanced at the maximum bandwidth conditions. The origin of this enhancement, as well as of the inversion of the tendency with the magnetic field, still lacks comprehensive explanation.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of the present paper is to achieve more quantitative understanding of the behavior of the SdHO under periodic modulation. In the previous works quoted above, [5][6][7][8][9] ULSLs with a large amplitude periodic modulation are employed, which is obviously advantageous in attaining the modulation of the SdHO strong enough to be readily observed. However, the amplitude of the periodic modulation or the width of Landau bands exceeding 10% of the Fermi energy seems to be rather incompatible with the perturbative treatment as in eq.…”

Section: Introductionmentioning

confidence: 99%

Modulation of the Shubnikov–de Haas Oscillation in Unidirectional Lateral Superlattices

Endo

Iye

2008

J. Phys. Soc. Jpn.

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The amplitude and phase of Shubnikov-de Haas oscillations have been analyzed in detail for two-dimensional electron gases subjected to a weak unidirectional periodic potential modulation. The amplitude is suppressed, accompanied by inversion of the phase, at the maximum bandwidth conditions at low magnetic fields. The suppression is gradually taken over by the enhancement with the increase of the magnetic fields. The suppression and the enhancement are attributable to the collisional and the diffusion contribution of the modulated potential to the conductivity, respectively, the former (the latter) being dominant at low (high) magnetic fields. A theoretical calculation that takes the two types of contributions into account shows semi-quantitative agreement with experimental traces.

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“…The planar geometry of a LSL is well-suited for experimental studies of the transport properties, and therefore the magnetotransport of both 1D and 2D LSLs, with the magnetic field B applied perpendicular to the 2DEG plane, have been the subject of extensive studies [see, e.g., Refs. 2,3,4,5,6,7,8,9,10,11,12,13,14,15 and Refs. 16,17,18,19,20 (and references therein) for 1D and 2D LSLs, respectively].…”

Section: Introductionmentioning

confidence: 99%

Fourier analyses of commensurability oscillations in Fibonacci lateral superlattices

Endo

Iye

2008

Phys. Rev. B

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Magnetotransport measurements have been performed on Fibonacci lateral superlattices (FLSLs) -two-dimensional electron gases subjected to a weak potential modulation arranged in the Fibonacci sequence, LSLLSLS..., with L/S=τ (the golden ratio). Complicated commensurability oscillation (CO) is observed, which can be accounted for as a superposition of a series of COs each arising from a sinusoidal modulation representing the characteristic length scale of one of the selfsimilar generations in the Fibonacci sequence. Individual CO components can be separated out from the magnetoresistance trace by performing a numerical Fourier band-pass filter. From the analysis of the amplitude of a single-component CO thus extracted, the magnitude of the corresponding Fourier component in the potential modulation can be evaluated. By examining all the Fourier contents observed in the magnetoresistance trace, the profile of the modulated potential seen by the electrons can be reconstructed with some remaining ambiguity about the interrelation of the phase between different components.

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Modulation of Landau levels by a one-dimensional periodic potential

Cited by 12 publications

References 8 publications

Weak localization and integer quantum Hall effect in a periodic potential

Weak localization and integer quantum Hall effect in a periodic potential

Modulation of the Shubnikov–de Haas Oscillation in Unidirectional Lateral Superlattices

Fourier analyses of commensurability oscillations in Fibonacci lateral superlattices

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