I will present the results of an extensive study of transport in the localised regime of mesoscopic two-dimensional electron systems (2DES) in modulation doped GaAs/AlGaAs heterojunctions. Disorder and interaction effects have been investigated by looking at the regime of low electron densities while systematically changing the strength of background disorder. The main focus will be on the observation of a low-temperature breakdown of the insulating phase in these systems. As the temperature decreases, a transition from insulating to metallic transport behaviour occurs, which persists even when the resistivity of the system greatly exceeds the quantum of resistivity $h/e^2$. par Furthermore, I will present results of magnetoresistance of hopping transport, where it was found that the average hopping distance was only determined by the average electron-electron separation, independent of the background disorder. Finally, a new kind of resistance oscillations will be discussed, which occur as a function of electron density and are induced by strong magnetic fields perpendicular to the 2DES.
Cavendish Laboratory, Cambridge University