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Quantum Hall Array

Superconducting graphene arrays (SUGAR)

The project will develop next-generation electrical resistance standards and thereby improve the realizations of resistance, current and mass. The technology is based on so-called Quantum Hall Arrays built with the nanomaterial graphene with superconducting contacts.

By utilizing manufacturing methods developed in collaboration with Chalmers, the project intends to develop the first large-scale Quantum Hall Arrays for the realization of resistance values down to 100 Ω, while also allowing for much higher bias currents than today. The Quantum Hall Arrays will be used to improve the realization of resistance and current and reduce the number of calibration steps, thus significantly reducing the measurement uncertainty. The technology also makes it possible to improve the realization of mass through a so-called Kibble balance (see below).

The project is part of RISE's investment in 2D materials and graphene.

Base units linked to physical constants of nature

The international system of units, SI, was last redefined in 2019. Since then, all base units have been linked to physical constants of nature via, among other things, quantum mechanical phenomena. One of these phenomena is the Quantum Hall Effect, which is used to realize the unit for resistance.

What is the Quantum Hall Effect?

The classic Hall effect occurs when you send a current through a conductor consisting of a 2D material (one or a few layers of atoms) that is affected by a magnetic field perpendicular to the surface of the conductor. When the electrons are affected by the magnetic field they move towards the sides of the conductor, so that one side of the conductor gets a positive charge and the other side a negative charge. A voltage then arises across the conductor, perpendicular to the direction of the current. This effect is linear. The stronger the magnetic field, the higher the voltage perpendicular to the direction of the current.

The classic Hall effect can be compared with a dimmer. When we turn the dimmer, the strength of the magnetic field changes and thus the voltage increases perpendicular to the direction of the current. But when we turn the dimmer so much that the magnetic field gets very strong, something happens. The voltage levels off and stays at one and the same level, or plateau. Then, as we continue to increase the strength of the magnetic field, the voltage makes a jump and stops at a new plateau, and so on. The resistance on each plateau then depends only on natural constants. It is this phenomenon that is called the Quantum Hall Effect.

The advantage of using the Quantum Hall Effect is that it provides very precise resistance levels that we can use in realizations of the unit. The disadvantage is that there are a limited number of resistance levels that are stable enough to be used in a metrology context. In practice, only a level close to 12.9 kΩ is used. Resistance standards at this level are then used to calibrate secondary standards to cover the entire resistance range. The chain of calibrations to reach low (<<100 Ω) and high resistance values (>>10 kΩ) increases the measurement uncertainty at each step.

Resistance standards at multiple levels

By connecting several conductors, or quantum Hall elements, to Quantum Hall Arrays, it becomes possible to find stable plateaus and realize electrical resistance values at basically any level. A resistance standard can then be compared directly with the Quantum Hall Array's resistance value, which allows us to produce primary resistance standards at more levels than today, without having to calibrate secondary standards to reach the desired resistance level. This significantly reduces measurement uncertainty.

Graphene and superconducting contacts

Although the principle of Quantum Hall Arrays has been demonstrated previously, technological limitations have meant that the use of Quantum Hall Arrays has not been established as an accepted method. But by combining the material graphene with superconducting contacts of, for example, niobium nitride, it is possible to produce stable Quantum Hall Arrays, as demonstrated on a smaller scale by NIST in the USA. The major challenges for producing Quantum Hall Arrays on a large scale are partly to ensure that all quantum hall elements are the same, and partly to develop a sufficiently robust process to avoid error sources when the elements are connected via electrical leads.

Also affects the Kibble balance and the realization of the kilogram

When the international system of units, SI, was redefined in 2019, the definition of mass was also changed from the international kilogram prototype (a metal cylinder of platinum and iridium stored in Paris since its creation in 1889) to be based on Planck's constant. At RISE we are developing a so-called Kibble balance to be able to realize the kilogram in the future. The Kibble balance involves measuring a current extremely accurately using a 100 Ω resistor. This resistor needs to be calibrated against a traditional quantum hall standard with a resistance value of 12.9 kΩ before each measurement. By replacing the resistor with a primary standard, one calibration step can be removed, which reduces the measurement uncertainty and thus improves the realization of the kilogram. The type of Kibble balance that RISE is developing requires a Quantum Hall Array with a resistance value of 100 Ω that can handle around 10 mA of current, which has not been achieved before.


Project name

Superconducting graphene arrays (SUGAR)



RISE role in project


Project start



Total budget

1 800 000 SEK





Project members

Contact person

Hans He


+46 10 516 61 38

Read more about Hans

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