Resistance quantization at zero magnetic field

The quantum anomalous Hall effect occurs in topological insulators. These are novel solid-state materials which were just discovered a few years ago and are conductive only at the surface. In the form of ferromagnetic thin layers, they exhibit a Hall resistance which is quantized at low temperatures without an exitternal magnetic field; this Hall resistance has the value of the von Klitzing constant h/e². For the investigations carried out by PTB, the topological insulator used was a ferromagnetic vanadium-(Bi_xSb_1–x)₂Te₃ mixed crystal which had been manufactured by molecular beam epitaxy (MBE) at the University of Würzburg. The anomalous Hall effect in this and similar materials and its theoretically predicted quantization without an external magnetic field had already been demonstrated for some time, but only with relative measurement uncertainties of approximately 10⁻⁴. If the effect were truly accurate, it could lead to future components in electrical quantum metrology in which quantum Hall resistance standards could be combined on one chip with Josephson voltage standards which only operate at zero magnetic field. However, manufacturing these crystals by MBE is so difficult that worldwide only very few research groups have mastered it. Moreover, the ferromagnetic state has been so sensitive up to now that, contrary to theoretical estimates, quantization occurs only at extremely low temperatures in the millikelvin range and at very small measuring currents of a few nanoamperes.

In cooperation with the Würzburg research group, quantization at zero magnetic field has now been demonstrated at currents of a few nanoamperes with a measurement uncertainty of 2.5 · 10^–7; this uncertainty is lower by nearly three orders of magnitude than previously obtained values. The measurements were made with the cryogenic current comparator bridge developed at PTB, which had already proven its value during the demonstration of the precise quantization of the fractional quantum Hall effect (see PTB-News, issue 1.2018).

The result obtained underpins the hope that the quantum anomalous Hall effect at zero magnetic field may in the future lead to electrical quantum standards that are simpler to operate, despite all the details of the effect still not being completely understood.