Physicists in Germany have developed a new way of defining the standard unit of electrical resistance. The advantage of the new technique is that because it is based on the quantum anomalous Hall effect rather than the ordinary quantum Hall effect, it does not require the use of applied magnetic fields. While the method in its current form requires ultracold temperatures, an improved version could allow quantum-based voltage and resistance standards to be integrated into a single, universal quantum electrical reference.
Since 2019, all base units in the International System of Units (SI) have been defined with reference to fundamental constants of nature. For example, the definition of the kilogram, which was previously based on a physical artefact (the international prototype kilogram), is now tied to Planck’s constant, h.
These new definitions do come with certain challenges. For example, today’s gold-standard way to experimentally determine the value of h (as well the elementary charge e, another base SI constant) is to measure a quantized electrical resistance (the von Klitzing constant RK = h/e2) and a quantized voltage (the Josephson constant KJ = 2e/h). With RK and KJ pinned down, scientists can then calculate e and h.
To measure RK with high precision, physicists use the fact that it is related to the quantized values of the Hall resistance of a two-dimensional electron system (such as the ones that form in semiconductor heterostructures) in the presence of a strong magnetic field. This quantized change in resistance is known as the quantum Hall effect (QHE), and in semiconductors like GaAs or AlGaAs, it shows up at fields of around 10 Tesla. In graphene, a two-dimensional carbon sheet, fields of about 5 T are typically required.
The problem with this method is that KJ is measured by means of a separate phenomenon known as the AC Josephson effect, and the large external magnetic fields that are so essential to the QHE measurement render Josephson devices inoperable. According to Charles Gould of the Institute for Topological Insulators at the University of Würzburg (JMU), who led the latest research effort, this makes it difficult to integrate a QHE-based resistance standard with the voltage standard.
A way to measure RK at zero external magnetic field
Relying on the quantum anomalous Hall effect (QAHE) instead would solve this problem. This variant of the QHE arises from electron transport phenomena recently identified in a family of materials known as ferromagnetic topological insulators. Such quantum spin Hall systems, as they are also known, conduct electricity along their (quantized) edge channels or surfaces, but act as insulators in their bulk. In these materials, spontaneous magnetization means the QAHE manifests as a quantization of resistance even at weak (or indeed zero) magnetic fields.
In the new work, Gould and colleagues made Hall resistance quantization measurements in the QAHE regime on a device made from V-doped (Bi,Sb)2Te3. These measurements showed that the relative deviation of the Hall resistance from RK at zero external magnetic field is just (4.4 ± 8.7) nΩ Ω−1. The method thus makes it possible to determine RK at zero magnetic field with the needed precision — something Gould says was not previously possible.
The snag is that the measurement only works under demanding experimental conditions: extremely low temperatures (below about 0.05 K) and low electrical currents (below 0.1 uA). “Ultimately, both these parameters will need to be significantly improved for any large-scale use,” Gould explains. “To compare, the QHE works at temperatures of 4.2 K and electrical currents of about 10 uA; making its detection much easier and cheaper to operate.”
Towards a universal electrical reference instrument
The new study, which is detailed in Nature Electronics, was made possible thanks to a collaboration between two teams, he adds. The first is at Würzburg, which has pioneered studies on electron transport in topological materials for some two decades. The second is at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig, which has been establishing QHE-based resistance standards for even longer. “Once the two teams became aware of each other’s work, the potential of a combined effort was obvious,” Gould says.
Because the project brings together two communities with very different working methods and procedures, they first had to find a window of operations where their work could co-exist. “As a simple example,” explains Gould, “the currents of ~100 nA used in the present study are considered extremely low for metrology, and extreme care was required to allow the measurement instrument to perform under such conditions. At the same time, this current is some 200 times larger than that typically used when studying topological properties of materials.”
As well as simplifying access to the constants h and e, Gould says the new work could lead to a universal electrical reference instrument based on the QAHE and the Josephson effect. Beyond that, it could even provide a quantum standard of voltage, resistance, and (by means of Ohm’s law) current, all in one compact experiment.
The possible applications of the QAHE in metrology have attracted a lot of attention from the European Union, he adds. “The result is a Europe-wide EURAMET metrology consortium QuAHMET aimed specifically at further exploiting the effect and operation of the new standard at more relaxed experimental conditions.”
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