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.

量子反常霍尔效应在计量学中具有潜在用途，因为它提供了在零外部磁场下根据 von Klitzing 常数（R_K = h/e²，其中 h 是普朗克常数，e 是基本电荷）进行霍尔电阻量子化的访问。然而，获得该效果具有挑战性，因为它需要低温（通常低于 50 mK）和低偏置电流（通常低于 1 μA）。在这里，我们报告了基于磁拓扑绝缘体 V 掺杂 （Bi，Sb）₂Te₃ 的器件上量子异常霍尔效应范围内的霍尔电阻量子化测量。我们表明，当外推到零测量电流时，霍尔电阻与 R_K 的相对偏差为 （4.4 ± 8.7） nΩ ^Ω−1，外推到零纵向电阻率时为 （8.6 ± 6.7） nΩ ^Ω−1（每个具有组合标准不确定性，k = 1）。这种 nΩ Ω⁻¹ 级（或 10⁻⁹ 的相对不确定度）的精度和准确度达到了相关计量应用所需的阈值，并建立了零外部磁场量子电阻标准，这对于将基于量子的电压和电阻标准集成到单个通用量子电参考中是必要的。