Interference phenomena due to a double bend in a quantum wire

Wu, Jong-Ching; Wybourne, M. N.; Yindeepol, W.; Weisshaar, A.; Goodnick, Stephen M.

doi:10.1063/1.105558

Cited by 75 publications

(44 citation statements)

References 13 publications

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“…In particular, Exner and Seba [5] have proved that the existence of a bound state for an electron confined to a planar waveguide, with curvature decaying at infinity and obeying Dirichlet boundary conditions at the border; Goldstone and Jaffe [6] have proved that an electron confined to an infinite tube of constant cross section, in two or more dimensions, has always a bound state, when the tube is not perfectly straight. The effect of bound states in infinite non-straight waveguides has been studied in [7,8,9,10,11,12]. It is worth mentioning a recent pedagogical article by Londergan and Murdock [13], that illustrates different numerical methods for the solutions of confined systems, in particular two-dimensional waveguides.…”

Section: Introductionmentioning

confidence: 99%

Weakly bound states in heterogeneous waveguides

2016

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Abstract. We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the heterogeneity corresponds to a locally denser material, the lowest eigenvalue of the spectrum falls below the continuum threshold and a bound state appears, localized at the heterogeneity. We devise a rigorous perturbation scheme and derive the exact expression for the energy to third order in the heterogeneity.

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Section: Introductionmentioning

confidence: 99%

Weakly bound states in heterogeneous waveguides

2016

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“…So we can obtain the equations for the coefficients in Eq. (4). Rewriting the resulted equations in the form of matrix, we can derive the transmission coefficient, τ m , by the scattering matrix method [21][22][23][24][25].…”

Section: Model and Formalismmentioning

confidence: 99%

“…The problem was firstly studied by Weisshaar et al [3] using modematching technique. The experiment work on the low temperature conductance of the double-bend waveguide was carried out by Wu et al [4] By using the recursive Greens function technique, Kawamura et al [5,6] studied this double-bend waveguide again. All the works showed strong resonant transmission due to internal reflections in the special structure and Refs.…”

Section: Introductionmentioning

confidence: 99%

Acoustic phonon transport through a double-bend quantum waveguide

Wang

Ding

2006

Physics Letters A

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In this work, using the scattering matrix method, we have investigated the transmission coefficients and the thermal conductivity in a double-bend waveguide structure. The transmission coefficients show strong resonances due to the scattering in the midsection of a double-bend structure; the positions and the widths of the resonance peaks are determined by the dimensions of the midsection of the structure. And the scattering in the double-bend structure makes the thermal conductivity decreases with the increasing of the temperature first, then increases after reaches a minimum. Furthermore, the investigations of the multiple double-bend structures indicate that the first additional double-bend structure suppresses the transmission coefficient and the frequency gap formed; and the additional double-bend structures determine the numbers of the resonance peaks at the frequency just above the gap region. These results could be useful for the design of phonon devices.

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“…A schematic view of a quantum heterostructure is shown in figure 2 following Wu et al [4] Electrons are emitted from the n-type doped AlGaAs layer, migrate into the GaAs layer and stay close to the boundary to the AlGaAs layer. In this way a very narrow layer of electrons which are free to move in a plane is formed.…”

Section: Tubes In Quantum Heterostructuresmentioning

confidence: 99%

Scattering in Quantum Tubes

Nilsson

2001

Foundations of Probability and Physics

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It is possible to fabricate mesoscopic structures where at least one of the dimensions is of the order of de Broglie wavelength for cold electrons. By using semiconductors, composed of more than one material combined with a metal slip-gate, two-dimensional quantum tubes may be built. We present a method for predicting the transmission of lowtemperature electrons in such a tube. This problem is mathematically related to the transmission of acoustic or electromagnetic waves in a twodimensional duct. The tube is asymptotically straight with a constant cross-section. Propagation properties for complicated tubes can be synthesised from corresponding results for more simple tubes by the so-called Building Block Method. Conformal mapping techniques are then applied to transform the simple tube with curvature and varying cross-section to a straight, constant cross-section, tube with variable refractive index. Stable formulations for the scattering operators in terms of ordinary differential equations are formulated by wave splitting using an invariant imbedding technique. The mathematical framework is also generalised to handle tubes with edges, which are of large technical interest. The numerical method consists of using a standard MATLAB ordinary differential equation solver for the truncated reflection and transmission matrices in a Fourier sine basis. It is proved that the numerical scheme converges with increasing truncation.

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Interference phenomena due to a double bend in a quantum wire

Cited by 75 publications

References 13 publications

Weakly bound states in heterogeneous waveguides

Weakly bound states in heterogeneous waveguides

Acoustic phonon transport through a double-bend quantum waveguide

Scattering in Quantum Tubes

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