Hall effect integer

The degree of precision of the quantized Hall effect has amaz-cd even the experts. Measured values of the Hall resistance at various integer plateaus are accurate to about one part in six million. The effect can be used to construct a laboratory standard of electrical resistance that is much more accurate than Ihe standard resistors currently in use. Authorities also observe that, if the quantized Hall effect is combined with a new calibration ol an absolute resistance standard, it should he able lo yield an improved measurement of the fundamental dimensionless constant of quantum electrodynamics. Ihe fine-structure constant or. 

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. 

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). 

Because of the massless Dirac fermions, graphene shows a variety of unusual electronic properties, such as an anomalous integer Quantum Hall Effect, absence of Anderson localization, a minimum conductivity , etc. These peculiarities in the electronic properties are described in dedieated reviews [10, 16]. 

More importantly, massless charge carriers in graphene can give rise to a room temperature quantum Hall effect (QHE) that was exclusively observed in two-dimensional electron gas (2DEG) systems earlier. The QHE on graphene is different from conventional cases of semiconductor heterostructures because of the unique band structure. Generally, the Hall resistance as a function of concentration of electrons produces a series of plateaus at jh/2eB, which is referred to as integer... 

Publishers Ltd., Nat. Mater., 6, Geim, A. K. and Novoselov, K. S., 183, Copyright 2007.) (b) The half-integer quantum Hall effect in graphene. (With permission from Macmillan Publishers Ltd., Nature, 438, Novoselov, K. S. et al., 197, Copyright 2005.)... 

Figure 7.13. Schematic representation of the integral quantum Hall effect. The plateaus in the Hall conductivity Pxy as a function of the magnetic field H, where its values are given by hle )l(l + 1) with Z + 1 an integer, are identified the diagonal conductivity pxx vanishes for the values of H corresponding to the plateaus.

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