Universality in scattering by large-scale potential fluctuations in two-dimensional conductors

TL;DR

This paper investigates electron scattering in two-dimensional conductors with large, opaque scatterers, revealing universal ratios of transport to quantum lifetimes dependent only on scattering type and dimensionality.

Contribution

It demonstrates that for convex scatterers, the ratio of transport to quantum lifetimes is universal, depending solely on scattering type and system dimensionality, regardless of scatterer shape.

Findings

a for D=3, b=2 for D=2 in specular scattering

The ratio a/b is shape-independent for convex scatterers

Discussion of classical-quantum scattering crossover

Abstract

We study electron propagation through a random array of rare, opaque and large (compared the de Broglie wavelength of electrons) scatterers. It is shown that for any convex scatterer the ratio of the transport to quantum lifetimes \eta=\tau_{tr}/\tau_{tot}$ does not depend on the shape of the scatterer but only on whether scattering is specular or diffuse and on the spatial dimensionality (D). In particular, for specular scattering, \eta is a universal constant determined only by the dimensionality of the system: \eta = 2 for D = 3 and \eta = 3/2 for D = 2. The crossover between classical and quantum regimes of scattering is discussed.