Electrons confined to two dimensions in a dela-doped heterostructure can arrange themselves in a droplet-like spatial distribution due to disorder and screening effects when their density is low. Application of this droplet picture to magnetotransport leads to several new interesting results and gives a good qualitative and quantitative account of recent experiments in such systems.

"Magnetically induced Coulomb blockade in small disordered delta-doped heterostructures",
V. Tripathi and M. P. Kennett, Phys. Rev. B 76, 115321 (2007). cond-mat/0702298.  

"Magnetotransport in disordered delta-doped heterostructures",
V. Tripathi and M. P. Kennett, Phys. Rev. B 74, 195334 (2006). cond-mat/0607263.  

Very interesting features are observed when two dimensional electron gases (2DEGs) are driven out of equilibrium with microwaves in a magnetic field, namely magnetoresistance oscillations (MRO) and zero resistance states (ZRS). I have studied the steady state set up when a 2DEG is driven by surface acoustic waves (SAWs). SAWs can couple to a 2DEG through the piezoelectric coupling in a GaAs heterostructure and generate an electric field in the 2DEG with the same temporal and spatial periodicity as the SAW. We have calculated the magnetoresistance of a 2DEG driven by SAWs and predict the existence of SAW-induced ZRS and MRO that differ from the microwave case in that they reflect geometric commensurability between the SAW wavelength and the electron cyclotron radius. These SAW-induced states should be observable in samples of similar quality to those in which microwave induced ZRS have been observed. The nature of disorder in the system alters the magnetoresistance trace - a naive model of isotropic scattering of electrons from impurities leads to different results than small-angle scattering (due to the long-range disorder potentials from remote dopants). However, the qualitative prediction of ZRS is robust under the two types of disorder.