chemical doping. This has been a topic of current research due to the versatile (some existing but mostly envisaged) applications of graphene. A separate class of heterostructures that can host 2DEGs are oxides. Although both sides of the heterostructure are insulators, the 2DEG at the interface may arise even without doping (which is the usual approach in semiconductors). Typical example is a ZnO/ZnMgO heterostructure. More examples can be found in a recent review including a notable discovery of 2004, a 2DEG at the LaAlO3/SrTiO3 interface which becomes superconducting at low temperatures. The origin of this 2DEG is still unknown, but it may be similar to modulation doping in semiconductors, with electric-field-induced oxygen vacancies acting as the dopants. Experiments Considerable research involving 2DEGs and 2DHGs has been done, and much continues to this day. 2DEGs offer a mature system of extremely high mobility electrons, especially at low temperatures. When cooled to 4 K, 2DEGs may have mobilities of the order of 1,000,000 cm2/Vs and lower temperatures can lead to further increase of still. Specially grown, state of the art heterostructures with mobilities around 30,000,000 cm2/(V·s) have been made. These enormous mobilities offer a test bed for exploring fundamental physics, since besides confinement and effective mass, the electrons do not interact with the semiconductor very often, sometimes traveling several micrometers before colliding; this so-called mean free path can be estimated in the parabolic band approximation as where is the electron density in the 2DEG. Note that typically depends on . Mobilities of 2DHG systems are smaller than those of most 2DEG systems, in part due to larger effective masses of holes (few 1000 cm2/(V·s) can already be considered high mobility). Aside from being in practically every semiconductor device in use today, two dimensional systems allow access to interesting physics. The quantum Hall effect was first observed in a 2DEG, which led to two Nobel Prizes in physics, of Klaus von Klitzing in 1985, and of Robert B. Laughlin, Horst L. Störmer and Daniel C. Tsui in 1998. Spectrum of a laterally modulated 2DEG (a two-dimensional superlattice) subject to magnetic field B can be represented as the Hofstadter's butterfly, a fractal structure in the energy vs B plot, signatures of which were observed in transport experiments. Many more interesting phenomena pertaining to 2DEG have been studied.[A] Footnotes A. Examples of more 2DEG physics. Full control of the 2DEG spin polarization was recently demonstrated.