Diffraction in the semiclassical description of mesoscopic devices

TL;DR

This paper extends the semiclassical description of mesoscopic devices to include diffraction effects caused by wedges and impurities, revealing how diffraction influences conductance and spectral properties.

Contribution

It derives formulas for diffraction matrices in pseudo integrable systems and demonstrates their impact on conductance and spectral decay behaviors.

Findings

Diffraction causes backscattering where semiclassical methods predict none.

Diffractive periodic orbits are detectable in the power spectrum.

Power spectrum decay rates indicate impurity and wedge scattering effects.

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 $\sim 1/l^{1/2}$ decay due to impurity scattering and $\sim 1/l^{3/2}$ decay due to wedge scattering. We think this is a universal sign of the presence of diffractive scattering in pseudo integrable waveguides.