Electrons Hall effect quantum

Ozyilmaz B, Jarillo-Herrero P, Efetov D et al (2007) Electronic transport and quantum hall effect in bipolar graphene p-n-p junctions. Phys Rev Lett 99 166804... 

The unique properties predicted for graphene comprise a number of very peculiar electronic properties—from an anomalous quantum Hall effect to the absence of localization. As new procedures for the large-scale production of graphene are expected to be developed in the near future, most of such properties—and those still unknown—will be soon experimentally demonstrated, thus permitting the development of the many important technological applications foreseen for this material. 

New physics such as the fractional quantum Hall effect has emerged from non-magnetic semiconductor heterostructures. These systems have also been a test bench for a number of new device concepts, among which are quantum well lasers and high electron mobility transistors. Ferromagnetic 111-Vs can add a new dimension to the III-V heterostructure systems because they can introduce magnetic cooperative phenomena that were not present in the conventional III-V materials. 

However, in the preceding two decades, there have been many experimental discoveries, beside high-Tc superconductivity, evidencing that we do not have yet the proper theoretical skills and tools to deal well with strongly correlated electron systems. For instance, heavy-fermions, fractional quantum Hall effect, ladder materials, and very specially high-Tc superconductivity seem not accessible from the weak coupling limit. 

Quantum-electrodynamics (QED) as the fundamental theory for electromagnetic interaction seems to be well understood. Numerous experiments in atomic physics as well as in high energy physics do not show any significant discrepancy between theoretical predictions and experimental results. The most striking example of agreement between theory and experiment represents the g factor of the free electron. The experimental value of g = 2.002 319 304 376 6 (87) [1] is confirmed by the calculated value of g = 2.002 319 304 307 0 (280) on the 10 11-level, where the fine structure constant as an input in the theoretical calculation was taken from the quantum Hall effect [2], Up to now uncalculated non-QED contributions play no important role. Indeed today experiment and theory of the free electron yield the most precise fine structure constant. 

The quantization of the Hall resistance in the FISDW phases is indeed very reminiscent of the quantum Hall effect in the two-dimensional electron gas [136]. There is, however, an important difference between these two phenomena. In both cases the quantization requires a reservoir of nonconducting electronic states. This reservoir is provided either by localized states in the gap between conducting Landau levels or by the electron-hole (spin modulation) condensate for the two-dimensional electron gas and the FISDW of organics, respectively. 

The Quantum Hall effect manifests itself in a two-dimensional electron gas in certain semiconductor structures. When such a structure is placed in a magnetic flux density normal to the plane of the electron gas, and a current I flows along its length, there is a quantized voltage Uh across the semiconductor in the direction perpendicular to the current given by... 

The integer quantum Hall effect can be understood in terms of noninteracting electrons, whereas the fractional effect is thought to result from many-electron interactions in two-dimensional systems, and to be an example of anyons see quantum statistics). 

Hausler, W., L. Kecke, and A.H. MacDonald. 2001. Strongly Correlated Electrons Mesoscopic Systems and Quantum Hall Effect, cond-mat/0108290. 

Keywords Garbon allotropes, graphene, graphene sheets, graphene oxide, quantum hall effect, drug delivery, bioimaging, cancer therapy, sensor, electronics, energy, catalysis, composites... 

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