Quantized Hall effect

K. von Klitzing (Stuttgart) discovery of the quantized Hall effect. 

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. 

Halperin, B, 1, The 1985 Noble Prize in Physics (Quantized Hall Effect), Science, 231, 820-822 (1986). 

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. 

For this example, Planck s constant from a watt-balance experiment, we first review the relevant descriptions of the Josephson effect and the Quantized Hall effect. 

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... 

Landau level A quantized energy level that occurs when an electrically charged particle is moving in an external magnetic field. The existence of such levels was predicted by Lev Landau in 1930. The concept of Landau levels is important in the theory of the quantum Hall effect. 

We want to derive the quantization of energy and flux of the Landau levels in the quantum Hall effect. Assume that the magnetic field is generated by a vector potential A = (-yH, 0,0), which is known as the Landau gauge. The Schrodinger equation for electrons confined in the xy plane is... 

With satisfaction we can also notice that the new field connected to the so-called "Quantized Hall effect" is on the program together with several other most important topics in atomic physics with bearing upon atomic constants and advanced physics metrology treated by pioneers in the fields. 

The last of the macroscopic quantum effect schemes that I shall mention is the one most recently discovered. Since the discoverer, von Klitzing, has a report following this one, my comments will be restricted to a few generalities. Essentially the Hall-effect resistance (i.e., the ratio of transverse voltage to longitudinal current) is quantized so that an vs. In curve exhibits steps in such a way that the ratio is a universal resistance [19], If this is expressed in terms of fundamental constants, one obtains ... 

This value is based on the assumption that q 14 is correct The uncertainty arises mainly from instabilities in the value of the calibrated reference resistor necessary for the determination of a (see Fig.3). A large number of theoretical papers discuss the question whether microscopic details of the semiconductor may influence the accuracy of Eq.l4. Up to now, no corrections to the value of the quantized Hall resistance are known, and the good agreement of the a- value deduced from the quantum Hall effect (Eq.l5) with the recommended value (Eq.l) and data obtained from other experiments ( q 4, Eq.7) demonstrates that corrections to the quantized Hall resistance (if any) should be smaller than the experimental uncertainty of about lO" . We believe that Eq.l4 is correct even at a higher level of accuracy and that the QHE can be used on one hand as a standard resistor (if the value for h/e is known or defined for metrological applications) and on the other hand for the determination of the fine-structure constant with an uncertainty corresponding to the uncertainty of the reference resistor. 

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