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

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, $\eta ={\tau }_{\mathrm{tr}}∕{\tau }_{\mathrm{tot}}$, does not depend on the shape of the scatterer but only on whether scattering is specular or diffuse and on the spatial dimensionality $\left(D\right)$. 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.

Figure 1

(Color online) Model of disorder.

Figure 2

Scattering by a convex object.

Figure 3

(Color online) Formation of a shadow by an opaque object.