Quantum Hall effects

D. Yoshioka, The Quantum Hall Effect, Springer, New York, 2002. 

M. Biittiker, The Quantum Hall Effects in Open Conductors... 

Novoselov KS, McCann E, Morozov SV et al (2006) Unconventional quantum Hall effect and Berry s phase of 2pi in bilayer graphene. Nat Phys 2 177-180... 

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... 

Shibata N, Nomura K (2009) Fractional quantum Hall effects of graphene and its bilayer. J Phys Soc Jpn 78 104708/1-104708/7... 

Darancet P, Wipf N, Berger C et al (2008) Quenching of the quantum Hall effect in multilayered epitaxial graphene the role of undoped planes. Phys Rev Lett 101 116806... 

Abanin DA, Novoselov KS, Zeitler U et al (2007) Dissipative quantum hall effect in graphene near the Dirac point. Phys Rev Lett 98 196806... 

Novoselov KS, Jiang Z, Zhang Y et al (2007) Room-temperature quantum hall effect in graphene. Science 315 1379... 

Williams JR, Dicarlo L, Marcus CM (2007) Quantum Hall effect in a gate-controlled p-n junction of graphene. Science 317 638-641... 

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. 

Eisensicin. J.F. and H.l. Siomtcr The Fractional Quantum Hall Effect. Senna. 1510 (June 2. I99l)i. 

PilKvok. A. and S. Das Surma Perspectives in Quantum Hall Effects. John Wiley Sons. Inc.. New York. NY. 1996. 

CTiakaraborty, T. and P. Pietilainen. The Fractional Quantum Hall Effect, Spiingei-Vedag, New York, NY, 1G88. 

Laughlin, R.B. The Relationship Between High-Temperature Superconductivity and die Fractional Quantum Hall Effect, 5 Science, 525 (October 28, 1988). 

The theory above has been applied in a variety of realistic situations. The range includes ionic conductance in aqueous solutions and molten alkali chlorides, damped spin-wave behaviour in paramagnetic systems, stimulated emission of radiation in masers, the fractional quantum Hall effect and quantum correlations in high-Tc cuprates and other non-BCS superconductors [4, 5, 7, 8, 14, 30]. In the next section we will also make some comments on the problem of long-range transcorrelations of protons in DNA [31]. 

E.J. Brandas, Quantum Correlations and Topological Quantum Numbers in the Fractional Quantum Hall Effect, Ber. Bunsenges. Phys. Chem. 96 (1992) 49. 

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. 

A comparison between theory and experiment for the fine structure intervals in helium holds the promise of providing a measurement of the fine structure constant a that would provide a significant test of other methods such as the ac Josephson effect the and quantum Hall effect. The latter two differ by 15 parts in 108 and are not in good agreement with each other [59]. 

Examples of the observational equations are given in Table 2. In that table, r H and vb are transition frequencies in hydrogen and deuterium such as those given in Table 3 below, Kj is the Josephson constant, which is characteristic of the Josephson effect, and Rk is the von Klitzing constant, which is characteristic of the quantum Hall effect. Note that Ex(riLj)/h is proportional to cRoo and independent of h, hence h is not an adjusted constant in these equations. 

To compare the theory of ae with experiment, it is necessary to know the value of a, which has been measured in diverse branches of physics. Currently best values of a, with relative standard uncertainty of 1 x 10-7 or less, are those based on the quantum Hall effect [32], the ac Josephson effect [25], the neutron de Broglie wavelength [33], the muonium hyperfine structure [34,35], and an absolute optical frequency measurement of the Cesium >1 line [36] ... 

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. 

There is also an integer or fractional quantum Hall effect, whereby in... 

Here p is either integer (p = 1,2,3, etc.) for the integer quantum Hall effect, first measured by von Klitzing25 at cryogenic temperatures [14], or a rational fraction (p 1 /3, 1/5, 5/2, etc.) for the fractional quantum Hall effect, first measured by Tsui, Stormer, and Laughlin [15]. The very well measured quantity ez/h = 25.81280745 kQ is called the von Klitzing constant, although it should also be called Landauer s constant. 

M. Biittiker, Absence of backscattering in the quantum Hall effect in multiprobe conductors, Phys. Rev. B38 9375-9389 (1988). 

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. 

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