A zero external magnetic field quantum standard of resistance at the 10⁻⁹ level

The quantum anomalous Hall effect is of potential use in metrology as it provides access to Hall resistance quantization in terms of the von Klitzing constant (R_K = h/e², where h is Planck’s constant and e the elementary charge) at zero external magnetic field. However, accessing the effect is challenging because it requires low temperatures (typically below 50 mK) and low bias currents (typically below 1 µA). Here we report Hall resistance quantization measurements in the quantum anomalous Hall effect regime on a device based on the magnetic topological insulator V-doped (Bi,Sb)₂Te₃. We show that the relative deviation of the Hall resistance from R_K at zero external magnetic field is (4.4 ± 8.7) nΩ Ω⁻¹ when extrapolated to zero measurement current and (8.6 ± 6.7) nΩ Ω⁻¹ when extrapolated to zero longitudinal resistivity (each with combined standard uncertainty, k = 1). This precision and accuracy at the nΩ Ω⁻¹ level (or 10⁻⁹ of relative uncertainty) reach the thresholds required for relevant metrological applications and establish a zero external magnetic field quantum standard of resistance, which is necessary for the integration of quantum-based voltage and resistance standards into a single universal quantum electrical reference.