In two-dimensional systems, perpendicular magnetic fields can induce a bulk band gap and chiral edge states, which gives rise to the quantum Hall effect. The quantum Hall effect is characterized by zero longitudinal resistance (R_xx) and Hall resistance (R_xy) plateaus quantized to h/(υe²) in the linear response regime, where υ is the Landau level filling factor, e is the elementary charge and h is Planck’s constant. Here we explore the nonlinear response of monolayer graphene when tuned to a quantum Hall state. We observe a third-order Hall effect that exhibits a nonzero voltage plateau scaling cubically with the probe current. By contrast, the third-order longitudinal voltage remains zero. The magnitude of the third-order response is insensitive to variations in magnetic field (down to ~5 T) and in temperature (up to ~60 K). Moreover, the third-order response emerges in graphene devices with a variety of geometries, different substrates and stacking configurations. We term the effect third-order nonlinear response of the quantum Hall state and propose that electron–electron interaction between the quantum Hall edge states is the origin of the nonlinear response of the quantum Hall state.

在二维系统中，垂直磁场可以感应出体带隙和手性边缘态，从而产生量子霍尔效应。量子霍尔效应的特征是在线性响应范围内将纵向电阻为零 （R_xx） 和霍尔电阻 （R_xy） 平台量化为 h/（υe²），其中 υ 是朗道能级填充因子，e 是基本电荷，h是普朗克常数。在这里，我们探讨了单层石墨烯在调谐到量子霍尔态时的非线性响应。我们观察到一个三阶霍尔效应，它表现出一个非零电压平台，随探针电流的立方缩放。相比之下，三阶纵向电压保持为零。三阶响应的大小对磁场（低至 ~5 T）和温度（高达 ~60 K）的变化不敏感。此外，三阶响应出现在具有各种几何形状、不同基板和堆叠配置的石墨烯器件中。我们将这种效应称为量子霍尔态的三阶非线性响应，并提出量子霍尔边缘态之间的电子-电子相互作用是量子霍尔态非线性响应的起源。