Electrons can be trapped at the interface between galliumarsenide and aluminumgalliumarsenide. As quantum mechanics forbids any motion perpendicular to the interface, these electron truly live in a twodimensional world. Applying a magnetic field perpendicular to the layer further restricts the quantum states and the physics becomes even more spectacular. For example, charge transport within the twodimensional system becomes quantized  a phenomenon known as the quantum Hall effect. Twodimensional electron systems formed in gallium arsenide represent an ideal laboratory to study manyparticle physics in lower dimensions.

We have recently applied our charge imaging method to the GaAs/AlGaAs system employing a 3D to 2D tunneling geometry. Using this novel technique, we have obtained the first direct images of ordered electronic structure within the interior. We find that the application of a magnetic field can produce surprising and subtle density variations, shown as bright and dark bands in the figure to the left. 
Gallium Arsenide Papers: Direct Observation of MicronScale Ordered Structure in a TwoDimensional Electron System, I. J. Maasilta, Subhasish Chakraborty, I. Kuljanishvili, S. H. Tessmer, and M. R. Melloch, Phys. Rev. B 68, 205328, 2003. Tunneling Images of a 2D Electron System in a Quantizing Magnetic Field, I. J. Maasilta, Subhasish Chakraborty, I. Kuljanishvili, S. H. Tessmer, and M. R. Melloch, Physica E 18, 167, 2003. Modeling Subsurface Charge Accumulation Images of a Quantum Hall Liquid, S. H. Tessmer, G. Finkelstein, P. I. Glicofridis, and R. C. Ashoori, Phys. Rev. B 66, 125308, 2002; also published in Virtual Journal of Nanoscale Science & Technology, 6/13, 2002. Imaging of Low Compressibility Strips in the Quantum Hall Liquid, G. Finkelstein, P. I. Glicofridis, S. H. Tessmer, R. C. Ashoori, and M. R. Melloch, Phys. Rev. B 61, R6323, 2000. Imaging the Low Compressibility Strips Formed by the Quantum Hall Liquid in a Smooth Potential Gradient,, G. Finkelstein, P. I. Glicofridis, S. H. Tessmer, R. C. Ashoori, and M. R. Melloch, Physica E 6, 251, 2000. Scanning Microscopes Probe Local Details of the Quantum Hall State, B. G. Levi, Physics Today (Search and Discovery) 51 (4), 17, 1998. Subsurface Charge Accumulation Imaging of a Quantum Hall Liquid, S. H. Tessmer, P. I. Glicofridis, R. C. Ashoori, L. S. Levitov, and M. R. Melloch, Nature 392, 5154 (1998); Nature 395, 724, 1998.