Prelocalization in semimetals

Abstract

The Fermi energy close to a band edge provides a conventional localization only when a one-dimensional residual resistance is large compared to $\frac{\pi \hslash }{e^2}$. Prior to the localization, the resistance increases first quadratically and then oscillates (between large and small values) with the length ("prelocalization"). There are several temperature regions, where the resistance may increase and decrease with temperature.