Diffraction in the semiclassical description of mesoscopic devices

Abstract

-In pseudo integrable systems diffractive scattering caused by wedges and impurities can be described within the framework of Geometric Theory of Diffraction (GDT) in a way similar to the one used in the Periodic Orbit Theory of Diffraction (POTD). We derive formulas expressing the reflection and transition matrix elements for one and many diffractive points and apply it for impurity and wedge diffraction. Diffraction can cause backscattering in situations, where usual semiclassical backscattering is absent causing an erodation of ideal conductance steps. The length of diffractive periodic orbits and diffractive loops can be detected in the power spectrum of the reflection matrix elements.The tail of the power spectrum shows ∼ 1/l 1/2 decay due to impurity scattering and ∼ 1/l 3/2 decay due to wedge scattering. We think this is a universal sign of the presence of diffractive scattering in pseudo integrable waveguides.In recent years, semiclassical methods became very popular in describing devices operating in the mesoscopic regime. There are two entirely different sets of theoretical tools which have been used in a wide range of applications. One of them is a WKB based short wavelength description [1, 2] where classical trajectories, chaos, regularity and analytic properties of the potential play a major role. The other is based on random matrix models or on averaging over random Gaussian potentials [3]. The first approach is designed to describe clean systems where the potential depends smoothly on coordinates and parameters, while the second assumes a system densely packed with impurities causing wild fluctuations of the potential on all length scales.Fortunately, advances in manufacturing and material design reduced the average number of impurities exponentially since the eighties and this trend is expected to continue in the future. Accordingly, a realistic semiclassical theory should be capable to treat systems with low number of impurities and not only completely clean or completely dirty ones. Another demand is that human designed structures,

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Negative Length Orbits in Normal-Superconductor Billiard Systems

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“…We have used this form of the GF in Ref. [16] to investigate the diffraction of the electron by the impurities, and in Ref. [17] to study the crossover behavior of the localization problem in a waveguide with periodically placed identical point-like impurities.…”