Is there a Metallic State in Two Dimensions?

Abstract

This paper reviews a series of experimental results on the metallic behaviour recently discovered in high quality, two-dimensional (2D) GaAs hole transistors. In particular, we address the question of what has happened to the two quantum corrections to the resistivity due to weak localisation and weak electron—electron interactions in the so-called metallic state. Detailed magnetoresistance data are presented just on the metallic side of the apparent metal—insulator transition, which show that both weak localisation (observed via negative magnetoresistance) and weak hole—hole interactions (giving a correction to the Hall constant) are present in the ‘metallic’ phase. The results suggest that as T→ 0 the resistivity will stop decreasing but turn up and tend towards infinity, in agreement with the early predictions of the one parameter scaling theory of localisation. The implication is that, even at high r _s , there is no metallic phase at T = 0 in two dimensions. Other unexplained features of the anomalous ‘metallic’ state are also discussed, such as the destruction of metallic behaviour by a parallel magnetic field.