Conductance of a single-mode electron waveguide with statistically identical rough boundaries

Makarov, N. M.; Tarasov, Yu. V.

doi:10.1088/0953-8984/10/7/006

Cited by 32 publications

(80 citation statements)

References 18 publications

(67 reference statements)

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“…the actual number of summands in the equations (4.19) and (4.20), is entirely determined by the width k c of the rectangular power spectrum (4.23b). It is clear that if the distance |k n −k n±1 | between neighboring quantum values of k n is larger than the correlation width k c , 24) then the transitions between all propagating modes are forbidden. As a consequence, the sum over n ′ in the expression (4.19) for the inverse forward scattering length contains only diagonal term with n ′ = n which describes direct intra-mode scattering inside the channels.…”

Section: Multimode Waveguidementioning

confidence: 99%

“…(ii) As is well known from the standard theory of 1D localization (see, e.g., [13,14,24]), the transport through any 1D disordered system is determined only by the backscattering length L n . Since the former diverges for every independent channel in line with the expression (4.25), all of them exhibit the ballistic transport with the partial average transmittance T n = 1.…”

Section: Multimode Waveguidementioning

confidence: 99%

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Anomalous transport in low-dimensional systems with correlated disorder

Izrailev¹,

Makarov²

2005

J. Phys. A: Math. Gen.

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Abstract. We review recent results on the anomalous transport in onedimensional and quasi-one-dimensional systems with bulk and surface disorder. Main attention is paid to the role of long-range correlations in random potentials for the bulk scattering, and in corrugated profiles for the surface scattering. It is shown that with a proper choice of correlations one can construct such a disorder that results in a selective transport with given properties. A particular interest is in the possibility to arrange windows of a complete transparency (or reflection) in the dependence on the wave number of incoming classical waves or electrons.

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Section: Multimode Waveguidementioning

confidence: 99%

Section: Multimode Waveguidementioning

confidence: 99%

Anomalous transport in low-dimensional systems with correlated disorder

Izrailev¹,

Makarov²

2005

J. Phys. A: Math. Gen.

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“…In particular, the transmission coefficient smoothly decreases with an increase of the angle of incoming waves, see details in [2,4]. Below we present an analytical treatment of the electron/wave scattering in waveguides with rough surfaces, paying main attention to the interplay between "amplitude" and "gradient" scattering mechanisms [5,6].…”

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confidence: 99%

“…The method we use is based on the coordinate transformation that makes both boundaries flat, (see for example, [6,7]),…”

mentioning

confidence: 99%

Rough surface scattering in many‐mode conducting channels: gradient versus amplitude scattering

Izrailev

Makarov

Rendón

2005

Physica Status Solidi (b)

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We study the effect of surface scattering on transport properties in many-mode conducting channels (electron waveguides). Assuming a strong roughness of the surface profiles, we show that there are two independent control parameters that determine statistical properties of the scattering.The first parameter is the ratio of the amplitude of the roughness to the transverse width of the waveguide. The second one, which is typically omitted, is determined by the mean value of the derivative of the profile. This parameter may be large, thus leading to specific properties of scattering. Our results may be used in experimental realizations of the surface scattering of electron waves, as well as for other applications (e.g., for optical and microwave waveguides).

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“…As was shown in Ref. [8], the perturbation approach is quite complicated and should be performed in a special way.…”

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confidence: 99%

Amplitude and gradient scattering in waveguides with corrugated surfaces

Izrailev

Luna‐Acosta

Méndez-Bermúdez

et al. 2003

phys. stat. sol. (c)

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We study chaotic properties of eigenstates for periodic quasi-1D waveguides with "regular" and "random" surfaces. Main attention is paid to the role of the so-called "gradient scattering" which is due to large gradients in the scattering walls. We demonstrate numerically and explain theoretically that the gradient scattering can be quite strong even if the amplitude of scattering profiles is very small in comparison with the width of waveguides. 05.45.Mt, 41.20.Jb, 42.25.Dd, 71.23.An During last decade much attention has been paid to the theory of quasi-1D disordered solids with the so-called bulk scattering. By this term one describes the situation where the whole volume of a scattering region contains scatters whose density determines the mean free path λ for a propagation of electrons. According to the theory, apart from λ, transport properties of finite samples are described by two other characteristic lengths: size L of a sample and localization length l ∞ . The latter is deterimied by the degree of the decrease of the amplitude of eigenstates along infinite samples with the same scattering characteristics. The core of the modern theory of the transport for such quasi-1D systems is the so-called single-parameter scaling. It was shown that when the mean free path is much less than both L and l ∞ , all statistical characteristics of the transport are fully described by the only scaling parameter which is the ratio of the localization length to the size of a sample (see, e.g. [1] and references therein).Another kind of quasi-1D systems that has attracted much attention in past few years, is the many-mode waveguide with rough surfaces. In this case the scattering is entirely related to statistical characteristics of scattering walls, therefore, one can speak about surface scattering. For some time it was believed that the surface scattering can be analytically described by modified methods thoroughly developed for bulk scattering. However, recent numerical studies of such systems [2,3] have revealed a principal difference between surface and bulk scattering (see discussion and references in [4]). Specifically, it was found that the transport through quasi-1D waveguides with rough surfaces essentially depends on many characteristic lengths, not on one length as in the case of the bulk scattering. This fact is due to a non-isotropic character of scattering in the channel space. In particular, the transmission coefficient smoothly decreases with an increase of the angle of incoming waves, since characterictic lengths for backscattering are different for different channels [3,5].The latter subject of the surface scattering has a direct link to the problem of quantum chaos. The point is that the waveguides with rough walls can be treated from the viewpoint of classical and quantum mechanics that describe a particle moving inside billiards and having multiple reflections from the walls. One of the problems of quantum chaos is the quantum-classical correspondence for the situation when, in the classical limit, glob...

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Conductance of a single-mode electron waveguide with statistically identical rough boundaries

Cited by 32 publications

References 18 publications

Anomalous transport in low-dimensional systems with correlated disorder

Anomalous transport in low-dimensional systems with correlated disorder

Rough surface scattering in many‐mode conducting channels: gradient versus amplitude scattering

Amplitude and gradient scattering in waveguides with corrugated surfaces

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