Anomalous Low-Field Classical Magnetoresistance in Two Dimensions

Дмитриев, А. П.; Dyakonov, Michel; Jullien, R.

doi:10.1103/physrevlett.89.266804

Cited by 50 publications

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“…Nevertheless, the dependance of these corrections on the magnetic field turns out to be very sharp, resulting in the MR anomaly. The anomaly was discovered in recent numerical simulations [15] where the MR in a system of 2D electrons scattering on randomly distributed hard disks was studied. This system is usually referred to as the Lorenz gas and is the simplest model of the 2D electron gas with strong scatterers.…”

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Anomalous negative magnetoresistance caused by non-Markovian effects

2003

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A theory of recently discovered anomalous low-field magnetoresistance is developed for the system of two-dimensional electrons scattered by hard disks of radius a, randomly distributed with concentration n. For small magnetic fields the magentoresistance is found to be parabolic and inversely proportional to the gas parameter, δρxx/ρ ∼ −(ωcτ ) 2 /na 2 . With increasing field the magnetoresistance becomes linear δρxx/ρ ∼ −ωcτ in a good agreement with the experiment and numerical simulations.

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“…The anomaly was observed in the case β ≪ 1, β 0 ≪ 1. Both the numerical simulations and the qualitative analysis of [15] indicated that at zero temperature, T, the MR can be expressed in terms of a dimensionless function f (z) via…”

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confidence: 99%

Anomalous negative magnetoresistance caused by non-Markovian effects

2003

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“…However, for B = 0 the role of ME is dramatically increased due to a strong dependence of return probability on B. Recent studies demonstrated that ME lead to a variety of nontrivial magnetotransport phenomena in 2D disordered systems such as magnetic-field-induced classical localization [7,8], high-field negative [7,8,9,10, 11] and positive MR [12], low-field anomalous MR [13,14,15], and non-Lorentzian shape of cyclotron resonance [16].In spite of large number of publications, devoted to the study of the influence of the nonMarkovian effects on the MR, the dependence of R on B, induced by such effects, was investigated (to the best of our knowledge) only in the context of so-called "circling electrons" [7]. These electrons occupy closed cyclotron orbits which avoid scatterers.…”

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“…1c ′ ) thus decreasing (increasing) S 0 and leading to a sharp dependence of W on B. The corresponding correction to ρ xx was calculated numerically in [13] and analytically in [14].…”

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Sharp magnetic field dependence of the two-dimensional Hall coefficient induced by classical memory effects

Дмитриев

Kachorovskii

2008

Phys. Rev. B

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We show that a sharp dependence of the Hall coefficient R on the magnetic field B arises in twodimensional electron systems with randomly located strong scatterers. The phenomenon is due to classical memory effects. We calculate analytically the dependence R(B) for the case of scattering by hard disks of radius a, randomly distributed with concentration n0 ≪ 1/a 2 . We demonstrate that in very weak magnetic fields (ωcτ n0a 2 ) memory effects lead to a considerable renormalization of the Boltzmann value of the Hall coefficient: δR/R ∼ 1. With increasing magnetic field, the relative correction to R decreases, then changes sign, and saturates at the value δR/R ∼ −n0a 2 . We also discuss the effect of the smooth disorder on the dependence of R on B.PACS numbers: 05.60.+w, 73.43.Qt, 73.50.Jt The simplest theoretical description of the magnetotransport properties of the twodimensional (2D) degenerated electron gas is based on the Boltzmann equation which yields the well-known expressions for the components of the resistivity tensor:Here τ is the transport scattering time, ω c = |e|B/mc is the cyclotron frequency, R = 1/enc < 0 is the Hall coefficient, and n is the electron concentration. Thus, in the frame of the Boltzmann approach, ρ xx and R do not depend on magnetic field B. Experimental measurements of ρ xx and R are widely used to find τ and n.It is known, that Eqs.(1) may become invalid due to a number of effects of both quantum and classical nature. The most remarkable of them is the Quantum Hall Effect. Another quantum effect, weak localization, leads to negative magnetoresistance (MR) -the decrease of ρ xx with B, concentrated in the region of weak magnetic fields [1]. Besides, the dependence of ρ xx on B appears due to quantum effects related to electron-electron interaction [2] (see also [3] for review). At the same time, both weak localization and electron-electron interaction (in frame of standard Altshuler-Aronov theory) do not result in any dependence of R on B (see [4] and [2,5,6], respectively).The dependence of ρ xx on B may also be caused by classical effects. One of the reasons is that in the Boltzmann approach one neglects classical memory effects (ME) arising as a manifestation of non-Markovian nature of electron dynamics in a static random potential. Physically, a diffusive electron returning to a certain region of space "remembers" the random potential landscape in this region, so its motion is not purely chaotic as it is assumed in the Boltzmann picture. For B = 0, non-Markovian corrections to kinetic coefficients are usually small. In particular, in a case of hard-core scatterers of radius a (impenetrable disks) randomly distributed with concentration n 0 , ME-induced relative correction to the resistivity is proportional to the gas parameter β 0 = a/l = 2n 0 a 2 ≪ 1 (l = 1/2an 0 is the mean free path). However, for B = 0 the role of ME is dramatically increased due to a strong dependence of return probability on B. Recent studies demonstrated that ME lead to a variety of nontrivial magnet...

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“…The observed LNMR, that is an anomalous behavior, reached up to 20 % of the zero field resistivity (ρ xx (B = 0)), however, in a very small region around B = 0, the resistivity showed a non-anomalous behavior. Recent theoretical developments for the conductivity of a classical two-dimensional Lorentz gas [8,9] allowed us to attribute this MR to non-Markovian memory effects originated by specific return processes in backscattering of electrons by corrugations and defects. However, a certain difference related to the order of magnitude of the full variation of ∆ρ xx /ρ xx (0) = [ρ xx (B) − ρ xx (0)]/ρ xx (0) appeared between the theoretical model and our experimental results.…”

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confidence: 99%