Magnetic localization of classical electrons in 2D disordered lattice

Baskin, E.; Éntin, M. V.

doi:10.1016/s0921-4526(98)00318-4

Cited by 35 publications

(32 citation statements)

References 3 publications

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“…6 is linked to the memory effects arising in backscattering events. It has a close relation to the well known nonanalyticity of the virial expansion of transport coefficients, 19-23 which we briefly recall.…”

Section: Qualitative Discussion Of the Problemmentioning

confidence: 99%

Non-Markovian effects on the two-dimensional magnetotransport: Low-field anomaly in magnetoresistance

2004

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We discuss classical magnetotransport in a two-dimensional system with strong scatterers. Even in the limit of very low field, when c Ӷ 1 ( c is the cyclotron frequency, is the scattering time) such a system demonstrates strong negative magnetoresistance caused by non-Markovian memory effects. A regular method for the calculation of non-Markovian corrections to the Drude conductivity is presented. A quantitative theory of the recently discovered anomalous low-field magnetoresistance is developed for the system of twodimensional 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,In some interval of magnetic fields the magnetoresistance is shown to be linear ␦ xx / ϳ − c in a good agreement with the experiment and numerical simulations. Magnetoresistance saturates for c ӷ na 2 , when the anomalous memory effects are totally destroyed by the magnetic field. We also discuss magnetotransport at very low fields and show that at such fields magnetoresistance is determined by the trajectories having a long Lyapunov region.The problem of magnetoresistance in metal and semiconductor structures has been intensively discussed in literature during the past three decades. A large number of both theoretical and experimental papers on this subject was published. Most of these works were devoted to the case of the degenerate two-dimensional electron gas where the electrons move in the plane perpendicular to the magnetic field and scatter on a random impurity potential. In this situation only the electrons with energy close to the Fermi energy participate in conductance and the usual approach based on the Boltzmann equation leads to vanishing magnetoresistance. In other words, the longitudinal resistance xx of the sample does not depend on the magnetic field B. This implies that the explanation of the experimentally observed B dependence of the longitudinal resistance should be sought beyond the Boltzmann theory.The intense exploration of this area began from the work of Altshuler et al. 1 where the experimentally observed in two-dimensional (2D) metals and semiconductor structures negative magnetoresistance (MR), i.e., decreasing xx with increasing B, was explained by quantum interference effects. It was shown that the magnetic field destroys the negative weak localization correction to the conductivity, thus resulting in decreasing longitudinal resistance. Since the first publication on the subject 1 a vast amount of work has been devoted to its further exploration (see for review Ref. 2).Two years prior to Ref. 1 there appeared a publication 3 where a classical mechanism of negative magnetoresistance was discussed. The mechanism was investigated on the example of a gas of noninteracting electrons scattering on hard disks (antidots). It was shown that with increasing magnetic field there is an increasing number of closed electron orbits which avoid scatterers and therefor...

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Section: Qualitative Discussion Of the Problemmentioning

confidence: 99%

Non-Markovian effects on the two-dimensional magnetotransport: Low-field anomaly in magnetoresistance

2004

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“…There are several distinct sources of a nontrivial MR, which reflect the rich physics of the magnetotransport in 2D systems. First of all, it has been recognized recently that even within the quasiclassical theory memory effects may lead to strong MR 3,4,5,6,7,8,9 . The essence of such effects is that a particle "keeps memory" about the presence (or absence) of a scatterer in a spatial region which it has already visited.…”

Section: Introductionmentioning

confidence: 99%

“…As a prominent example, memory effects in magnetotransport of composite fermions subject to an effective smooth random magnetic field explain a positive MR around half-filling of the lowest Landau level 7 . Another type of memory effects taking place in systems with rare strong scatterers is responsible for a negative MR in disordered antidot arrays 3,4,5,8,9 . However, such effects turn out to be of a relatively minor importance for the low-field quasiclassical magnetotransport in semiconductor heterostructures with typical experimental parameters, while at higher B they are obscured by the development of the Shubnikovde Haas oscillation (SdHO).…”

Section: Introductionmentioning

confidence: 99%

Interaction-induced magnetoresistance in a two-dimensional electron gas

2004

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We study the interaction-induced quantum correction δσ αβ to the conductivity tensor of electrons in two dimensions for arbitrary T τ (where T is the temperature and τ the transport scattering time), magnetic field, and type of disorder. A general theory is developed, allowing us to express δσ αβ in terms of classical propagators ("ballistic diffusons"). The formalism is used to calculate the interaction contribution to the longitudinal and the Hall resistivities in a transverse magnetic field in the whole range of temperature from the diffusive (T τ ≪ 1) to the ballistic (T τ 1) regime, both in smooth disorder and in the presence of short-range scatterers. Further, we apply the formalism to anisotropic systems and demonstrate that the interaction induces novel quantum oscillations in the resistivity of lateral superlattices.

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“…The result is plotted in Fig. 2b for sample D4, showing a Drude-like response with very little dependence on B except near B = 0 T where quantum phase coherent effects such as weak localization [21][22][23] and memory effects [24][25][26][27] as well as electron-electron interactions [28,29] may play a role. We will there -FIG.…”

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confidence: 99%