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Experimental test of the fractional quantum Hall effect

Resistance quantization demonstrated with great accuracy

PTB-News 1.2018
Especially interesting for

resistance metrology

solid-state physics

The “new SI”, scheduled for May 2019, is based on fundamental constants which can be directly measured by means of macroscopic quantum effects. Verifying the theoretical fundaments of these effects experimentally with the greatest accuracy is one of the core tasks of metrology. In the case of the quantum Hall effect, this has now been successfully done for the first time for a state in which the current is no longer carried by electrons, but by quasi-particles of magnetic flux quanta and electrons.

In certain magnetic field ranges, fractional (blue curve) and integer QHE lead to resistance values that are only given by the fundamental constants h and e, and by a rational number. The ratio of 1 : 6, which had been predicted theoretically for the two resistance values characterized by the two arrows, has been experimentally confirmed for the first time with a measurement uncertainty of a few parts in 108. The inserted image is a schematic representation of the composite fermion in this fractional QHE regime. The quasi-particle consists of an electron to which two magnetic flux quanta are bound; it carries the charge e/3.

In the case of the quantum Hall effect (QHE), electric resistance only depends on the values of Planck’s constant h and of the elementary charge e. In the case of the Josephson effect, these two constants (h and e) also play a decisive role – in this case, however, for the realization of electric voltages. Since h will also be the basis for the future definition of the kilogram, the two electric quantum effects play a key role in the new system of units (SI) which is based on fundamental constants. The importance of the QHE is essentially due to the theoretically predicted universality with which resistance values are quantized in certain ranges of magnetic fields. In the case of the “regular” (integer) QHE, the quantized resistance values amount to 1/i RK, where i is an integer and the von Klitzing constant is RK = h/e2.

High-precision measurements were carried out at PTB for the first time in a special regime of the QHE where the current is no longer carried by electrons but by quasi-particles formed by a “cluster” of electrons and magnetic flux quanta. The charge of these quasi-particles designated as “composite fermions” corresponds to rational fractions of the elementary charge. In this exotic regime, the QHE exhibits quantized resistance values given by rational fractions of the von Klitzing constant and is therefore called fractional QHE.

Measuring this resistance accurately requires extremely pure semiconductor samples in which the composite particles form at very low temperatures of a few hundredths of degrees above absolute zero and at even higher magnetic fields than for the integer QHE. It has been possible to achieve these experimental conditions for several years. The limitation of the current used for the measurement to less than a hundredth of the usual current is much more critical. If the current is too high, the composite fermions will basically “melt” during the measurement; if the current is too low, the measurement uncertainties can become very high.

To solve this problem, PTB’s improvement of electrical resistance bridges based on cryogenic current comparators (CCC) was crucial. Considerable improvements of the bridge now allow the achievement of relative measurement uncertainties of a few parts in 108 even at currents in the nanoampere range. The universality of resistance quantization could thus be demonstrated also in the fractional QHE regime with a relative uncertainty of 6.3 · 10–8.


Franz Ahlers
Department 2.6
Electrical Quantum Metrology
Phone: +49 531 592-2600

Scientific publication

F. J. Ahlers, M. Götz, K. Pierz: Direct comparison of fractional and integer quantized Hall resistance. Metrologia 54, 516–523 (2017)