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，垂直磁场可以引起体带隙和手性边缘态，从而产生量子霍尔效应。量子霍尔效应的特点是零纵向电阻 ( R _xx ) 和霍尔电阻 ( R _xy ) 平台在线性响应区域中量化为h /( υe ² )，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，我们探索单层石墨烯调谐到量子霍尔态时的非线性响应。我们观察到三阶霍尔效应，该效应表现出与探头电流呈三次方比例关系的非零电压平台。相比之下，三阶纵向电压保持为零。三阶响应的幅度对磁场（低至约 5 T）和温度（高至约 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、不同基底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根源。