  We review some of our recent experimental studies on low-carrier
concentration, mesoscopic two-dimensional electron gases (m2DEGs). The m2DEGs
show a range of striking characteristics including a complete avoidance of the
strongly localised regime even when the electrical resistivity $\rho >> h/e^2$,
giant thermoelectric response, and an apparent decoupling of charge and
thermoelectric transport. We analyse the results and demonstrate that these
observations can be explained based on the assumption that the charge carriers
retain phase coherence over the m2DEG dimensions. Intriguingly, this would
imply phase coherence on lengthscales of up to 10 $\mu$m and temperature $T$ up
to 10 K which is significantly greater than conventionally expected in
GaAs-based 2DEGs. Such unprecedentedly large phase coherence lengths open up
several possibilities in quantum information and computation schemes.
