The kilogram is currently defined by a lump of metal in Paris – but now researchers in the UK, France and Sweden have confirmed a key assumption of a new method of defining the standard based on fundamental constants. Specifically, they have shown that the quantum Hall resistances measured in a semiconductor and in graphene are identical up to a relative uncertainty of 8.6 × 10–11. This resistance is given by the ratio of the Planck constant (h) to the square of electron charge (e) and can be used to define the kilogram.

The kilogram standard is made from platinum and iridium, and is housed at the International Bureau of Weights and Measures (BIPM) in Paris. Over the past 60 years, several comparisons of this kilogram with identical copies suggest that its mass is changing. As a result, scientists have been looking for a new way to define the kilogram using just fundamental constants.

The most popular way of trying to do this is with a "watt balance", which compares the weight of an object with an electromagnetic force. Such a balance operates on the assumption that the ratio of h/e2 is independent of the material used to measure it. A watt balance uses this ratio along with a measurement of the quantum Hall resistance to define the kilogram in terms of h.

### Drifting electrons

The Hall effect is the appearance of a voltage across opposite faces of a sheet of metal when a current passes along its length. The effect requires the presence of a magnetic field that is perpendicular to the sheet. The magnetic field causes the moving electrons to drift towards one face as they cross the sheet of metal. Ordinarily, the electron's tendency to drift depends on factors such as the density of electrons in the material and the thickness of the sheet.

The quantum Hall effect occurs in sheets that are so thin that they appear 2D to the electrons. If such a sheet is subject to very low temperatures and high magnetic fields, the Hall voltage is quantized at discreet values that appear to be independent of the material used. When the Hall voltage is compared with the current running through the conductor, the resulting Hall resistance is simply h/Ne2, with N being an integer.

According to J T Janssen of the National Physical Laboratory (NPL) in Teddington, UK, there is no theory to explain why this should be the case; however, all experiments so far agree on this universal value for the quantum Hall resistance. If the redefinition of the kilogram is to rest on the quantum Hall effect, then the uncertainties in these experiments must be very stringent indeed.

### Direct comparison

Now Janssen and colleagues at the NPL, Chalmers University and Linköping University in Sweden, the University Lancaster in the UK and the BIPM have made a direct comparison of the quantum Hall effect of two very different materials. These are a gallium–arsenide semiconductor doped to produce a 2D sheet of electrons, and graphene – which is a single layer of carbon atoms. Previous experiments have confirmed that two semiconductors exhibit the same quantum Hall effect, but this new work is the first to directly compare two materials with very different electronic properties. While the conduction electrons in gallium arsenide behave like particles with mass, the electrons in graphene behave like massless photons.

The researchers use a standard set-up that compares the Hall resistances of two samples held at temperatures within a couple of degrees of absolute zero. Identical currents are sent through the samples to create the Hall voltages. To see whether these voltages are different, another circuit connects the sides of the two samples with an extremely sensitive current detector. No current was measured, meaning that the voltages across the samples were identical.

### Challenges remain

"This is the most precise measurement of the material independence of the quantum Hall effect," says Janssen. However, there are still important challenges to be overcome in the design and operation of the watt balance. The most significant, according to Janssen, is the mechanical challenge of operating the balance. For example, the force produced by the magnetic coil and its velocity must be carefully aligned with gravity. And as the overall uncertainty is reduced, it gets ever harder to make these alignments.

"The redefinition of the kilogram standard now is the one of the main topics in metrology," says Alexander Penin of the University of Alberta in Edmonton, Canada. Indeed, next week, metrologists will gather in Paris for the 24th General Conference on Weights and Measures to discuss the merits of the watt balance and other proposals for redefining the kilogram.

The work is described in New Journal of Physics 13 093026.

Janssen describes his work in the video abstract above.