Hall resistance, quantized

K. von Klitzing, G. Dorda, and M. Pepper, M. (1980). New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45 494 97 (1980). 

Fig. 3 Experimental set-up for measurements of the fine-structure constant using the quantum Hall effeet. % is the quantized Hall resistance, the standard resistance, and S is a two-way selector switch.

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. 

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. 

A direct consequence of the field-dependent Q vector is the quantization of the Hall resistance at pxy = hllNe2 (where the factor 2 comes from spin... 

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. 

Fig, 3. Hall resistance versus magnetic field along the c axis for two (TMTSF PFg samples (P 9 kbar, T = 0.5 K). The quantized values, h/2ne2=12.9/n kQ per molecular layer, are marked on the right for sample 1. The n = 0 phase is reached above 18 T (left). Magnetoresistance of the same sample up to 25 T (right linear scale in the inset). 

Hall coefficient, rare earth elements, 4-127 to 132 Hall density, superconductors, 12-73 to 74 Hall resistance, quantized, 1-1 to 11 Halocarbon refrigerants, 6-133 to 135 Handling and Disposal of Chemicals in Laboratories, 16-1 to 12... 

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 ... 

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